Extra-dimensional models on the lattice and the Layer Phase. Petros Dimopoulos
|
|
- Marlene Higgins
- 6 years ago
- Views:
Transcription
1 Extra-dimensional models on the lattice and the Layer Phase Petros Dimopoulos Frascati, 7/6/008
2 OUTLINE Introductory hints on the extra dimensional theories Models with extra dimension on the lattice; inclusion of anisotropic couplings in the action Pure U() model in D and the Layer phase D anisotropic Abelian-Higgs model: The Higgs Layer phase D SU()-Higgs model in the adjoint representation Remarks & Conclusions
3 Extra dimensions As far as it is known, there is not any fundamental principle for which the space-time should be 3+ dimensional Hence, it might be legitimate to assume extra spatial dimensions. It can not be denied that, up to now, the theoretical exploration of extra dimensional models is rather speculative than based on well established facts. Nevertheless, the construction of the extra dimensional models is guided by the requirement of physical consistency in order to show possible ways on how the extra dimensions can be revealed (or why are hidden) and to connect the extra-dimensional models with a more fundamental theory in order to solve long-standing theoretical problems.
4 Kaluza-Klein proposal (90, 96): Consider a five-dimensional flat space with the fifth dimension compactified The photon resides in the extra dimension The unification of gravity with electromagnetism can be achieved Extra dimensions à la Kaluza-Klein are hidden as a result of their size : l ~ 0-33 cm. Need for energies as high as the Planck energy to make them detectable.
5 Large Extra dimensions The idea of models with Large Extra dimensions is connected with the Brane world picture The ordinary matter (with exception of gravitons) is localised to a 3-D submanifold (brane) embedded in a fundamental multi-dimensional space (bulk) It is assumed that the brane picture is an effective model representation. It comes from a high-energy theory which appears at a fundamental scale M * The large extra dimensions should be so large as to non contradict the observations For compactified extra dimensions their size can be as big as a fraction of millimeter
6 Large Extra dimensions (continue) One of the main motivations for the Brane picture used in higher dimensional models is to give an answer to the : Hierarchy Problem Why M Pl >> M EW? Possible answer: The fundamental scale is M * ~ TeV in a theory defined in a 4+n space ADD model Arkani-Hamed, Dimopoulos & Dvali Phys.Lett.B 998 RS models Randall & Sundrum Phys.Rev.Lett. 998
7 ADD model Consider a flat brane (no brane tension) embedded in a 4+n space-time Standard matter resides on the brane Gravity spreads in the bulk The extra dimensions are compactified The metric does not depend on the extra coordinates Define a unique fundamental scale M * Volumetric scaling: M Pl = M n+ * V δ It is sufficient to assume n and R~0. mm for getting M * TeV
8 RS model Consider a five-dimensional anti de Sitter space the extra dimension obeys to z = z + π & z -z (S /Z orbifolded) negative cosmological constant in the bulk Assume the existence of two branes resided along the extra dimension and having opposite value of tension. Matter is assumed on the branes while the gravity can be spread in the bulk It is shown that the metric admitted for this set-up takes the form: ds = ω (z) η µν dx µ dx ν dz (with ω (z) = e The extra dimension becomes warped as a price of maintaining a 4D Lorentz space at every point of the extra dimension (non-factorizable geometry). The model provides an exponential hierarchy expressed by the distance which separates the two branes along the extra coordinate: -k z ) M Pl ~ e kzc M *
9 (Non) Renormalisability The couplings defined in extra dimensional theories are of negative mass dimension The current attitude is to make the conjecture to treat these theories as effective theories for energy scales up to /n E ~ /g (n is the mass dimension of the coupling) For bigger energies the effective theory has to be replaced by a more fundamental theory.
10 (4+)-dimensional pure U() gauge model
11 The gauge field in extra dimensional space What about a possible extension of the gauge field in the bulk? Is there any possibility of gauge localisation on the brane in the RS set-up? The answer given in terms of analytical work is negative Pomarol, Phys.Lett.B000 Davoudias, Hewett & Rizzo, Phys.Lett.B000 But since the localisation of the gauge field on the brane may involve strong coupling dynamics along the extra dimensions, the non-perturbative methods are necessary for giving an answer.
12 Abelian Gauge field in the RS background kz Assume the RS metric : ds = e ( dx dx dx dx ) dz 0 3 Consider a -dim abelian gauge model in the background of the RS metric: S gauge = 4g = d 4 d xdz 4g x g F F µν MN F κλ F η KQ µκ η g νλ MK g NQ g e kz F µ F ν η µν In the Euclidean space the gauge action reads: E k x S = d x F F + e F F µ, ν =,...,4 4g g gauge µν κλ µ µ We get a model with two different couplings, one defined on the 4D subspace and the second (bigger ) along the extra dimension. P.D., K. Farakos, A. Kehagias and G. Koutsoumbas NPB 00
13 On the lattice we define the pure U() Wilson gauge action with anisotropic couplings: S gauge = β ( ReU (x)) + β ( ReU (x)) µν µ x, µ < ν 4 x, µ 4 Link variables: Plaquettes: iasaµ ia { U e, U e A = } µ U = = M U U µν µ (x) = U (x) = U µ µ (x)u (x)u ν (x + a (x + a s s µˆ)u µˆ)u µ µ (x + a (x + a s νˆ)u ˆ)U ν (x) (x) The Fu-Nielsen proposal for dimensional reduction from lattice anisotropic models ( couplings β β ) Fu and Nielsen NPB 984, 98 Phase diagram becomes richer: A new phase appears
14 LAYER PHASE (I) Confining phase For β 0 and β =0 phase diagram of the 4D isotropic model 4D Coulomb phase Confining phase For β = β phase diagram of the D isotropic model D Coulomb phase Confining phase 4D Coulomb phase For β β β phase diagram of the D anisotropic model Layer phase Confining extra dimension D Coulomb phase
15 LAYER PHASE (II) The potential between heavy test charges is closely connected with the Wilson loops: W W W W µν µν µν µ (L, L ) exp (L, L ) exp (L, L ) exp (L, L ) exp [ σl L ] [ τ(l + L )] [ τ(l + L )] [ σ (L + L )] (Confining (Coulomb phase, phase, Layer phase µ, ν µ, ν ) ) Phase Diagram from Mean Field analysis D-Coulomb Confining phase Fu and Nielsen NPB 984, 98
16 Phase Diagram Monte Carlo Study Basic order parameters 4D (or space) plaquette : extra dimension (or transverse) plaquette : Pˆ Pˆ S 6N 4N x, µ < ν 4 x, µ 4 cos (F cos (F µ µν (x)) (x)) P = S PˆS P = Pˆ Behaviour of the Plaquette in the two limits of the coupling values P = β/ + O( β Dβ ) + O( β ) [ β<<, strong coupling ] [ β>>, weak coupling ] D is the dimension of the space
17 β =.0 Confining D Coulomb Phase Transition ~ [-(/β)] : D-Coulomb phase ~ β /: Confining phase P.D.,Farakos, Kehagias and Koutsoumbas NPB 00 Hulsebos, Korthals-Altes and Nicolis NPB 99 Big hysteresis loop Two-state signal st order PT
18 Confining Layer Phase Transition There is very strong evidence that the 4D Confining Coulomb phase transition is first order and takes place at β=.033() (β =0). [Arnold, Bunk, Lippert and Schilling 003] What does it happen as β > 0? We do an extensive study of the PT for two values of β =0.0 and 0. while we let β variable.
19 Confining Layer Phase Transition (continue) β =0. As the lattice volume becomes bigger the transition becomes steeper For β<<, P β/ S : Confining phase For β>>, P S (-/4β) : 4D-Coulomb phase For all β, P β /=0. (constant) extra dimension is confined!!
20 Identification of the phases using the helicity modulus The helicity modulus is an order parameter; it gives the response of the system to an external elecrtomagnetic flow. It is defined through the second derivative of the free energy: [Vettorazzo and de Forcrand, NPB 004 ] F( Φ ) h ( β ) = Φ Φ= 0 β =0. In the confinement phase the system does not feel any changes due to the external flux. On the contrary in the Coulomb phase the system reveals a response. h(β) 0 in the Coulomb phase h(β) = 0 in the confining phase The space-like and the transverse-like helicity modulus are: Helicity modulus in the transverse direction, h T takes zero value for all values of β. h ( β ) = (β cos(f )) (β sin(f )) S µν µν (Lµ Lν ) P P h = ( β ) (β cos(fµ )) (β sin(fµ )) (L L ) µ P P Confinement along the extra dimension
21 Confining Layer Phase Transition (continue) Distribution of the space-like plaquette: Two-state signal Susceptibility of the space-like plaquette S(Pˆ S ) V Pˆ S Pˆ S A net increase with the volume appears
22 Confining Layer Phase Transition (continue) The relative analysis shows that: The transition between the Confining phase and the Layer phase is of st order (though weak) as it happens to be the phase transition between the confining and the Coulomb phases for the 4D model. The transition points of the 4D gauge coupling almost lie on the horizontal line the initial point of which is critical value of the pure 4D model. Hence the Layer phase is completely distinguished from the confining one. P.D., Farakos, Vrentzos Phys.Rev.D 006
23 Layer D Coulomb Phase Transition β=.4 As the system passes to the D-Coulomb phase the extra fifth dimension ceases to be confined : h passes from zero to a non-zero value
24 Layer D Coulomb Phase Transition (continue) The susceptibility of the tranverse-like plaquette is: S(Pˆ ) V Pˆ Pˆ An increase of the susceptibility peaks, though weak, with the volume is observed. δ S ~ V, δ < max
25 Layer D Coulomb Phase Transition (continue) A finite scaling analysis assumes: β (L) = β (+ C L S = C + C max 0 L γ/ν -(/v) ) ν 0.7() β = 0.308(3) γ =.4(44) = δ = 0.44() Evidence for a nd PT * Volumes bigger than V=4 have to be used in order to confirm this evidence
26 It can be shown numerically on the lattice: how it can be identified a phase (Layer) which is coulombic on the four-dimensional subspace while it exhibits confinement along the extra dimension The Layer phase is stable and it is well separated from the confinement phase and the five-dimensional Coulomb phase the potential between two test charges in the layer phase is that of a 4D Coulomb interaction (~/r) and it is distinguishable from the potential of the D Coulomb phase (which goes as ~/r ) ( Farakos and Vrentzos, Phys.Rev.D 008)
27 (4+)-dimensional Abelian Higgs model
28 D anisotropic U()-Higgs model Assume a U()-Higgs model in five dimensions in the RS background A general metric of the RS type (warped extra dimension) is written as: ds = ω (z) [ dx dx ] dz ( ω 0 for z ) (z) 0 Write the action of a five-dimensional Abelian Higgs model (in this background): S = = = S + gauge 4 g d xdz d S d xdz scalar x 4 g * ΜΝ [ D Φ D Φ g V ( Φ )] * µν 4 * 4 [ D Φ D Φ η a ( z) D Φ D Φ a ( z) V ( Φ )] µ g F ( Μ, Ν = 0,...,4 and µ, ν = 0,...,3 ) F ΜΝ µν ν F F ΚΛ κλ η g µκ ΜΚ η g νλ ΝΛ + d x a ( z) F g z µ z g F ν η M µν + Ν
29 Make the rescaling α(z)φ =ϕ and consider a quartic scalar potential. The scalar action reads: S scalar = d 4 xdz * µ * * * [ D ϕ D ϕ a (z)d ϕ D ϕ M(z) ϕ ϕ λ( ϕ ϕ) ] µ [ ] + a (z) [ a (z)] with M(z) = a (z) m + z z Translate the action on the lattice and we get: S Lattice = S = β + β gauge + β + x h (we set : + S ( cosu (x)) + β ( cosu (x)) µν g µ g x, µ < ν 4 * [ ϕ (x) U (x) ϕ (x + aµˆ) ] [ ϕ (x) U (x) ϕ (x + aµˆ) ] L µˆ L L µˆ L h x, µ < ν 4 a * [ ϕ (x) U (x) ϕ (x + aˆ) ] [ ϕ (x) U (x) ϕ (x + aˆ) ] L L L L * m ϕ (x) ϕ (x) + β / x L 3/ scalar L ϕ = ϕ ) L L ˆ R * ( ϕ (x) ϕ (x)) L x,µ L The lattice couplings obey certain equations which depend on the warp factor: R β g = a (x )βg βh = a (x )β h λ = a M (x ) = βh 4β Due to the assumed function of the warp factor, the couplings for both the gauge and the scalar fileds along the extra dimension are strongly coupled. a ˆ β h m L
30 We adopt a simplified version for the lattice model under study: the couplings along the extra dimension do not depend on the extra coordinate but they are allowed to get different values from the couplings defined on the four dimensional subspace. The lattice action reads: S Lattice = = S β β h β gauge x h + S g x, µ < ν 4 scalar ( cos U (x) ) + β ( cos U (x) ) µν g µ * Re 4ϕ L (x) ϕ L (x) x, µ x µ 4 * ϕ (x)u ϕ (x + aµˆ ) * * Re [ 4ϕ ] L (x) ϕ L (x) ϕ L (x)u ϕ L (x + aˆ ) ˆ x * * [( β 4β β ) ϕ (x) ϕ (x) + β ( ϕ (x) ϕ (x) ) ] R h h L L R L L L µˆ L an extension of the initial proposal of Fu and Nielsen to the Abelian Higgs model
31 For the full phase diagram we need to study five couplings (!) β, β, β, β g g h h and β R We can make a reasonable compromise : keep small: β h << take β g < in order to have the possibility to get a confinement phase in the four-dimensional subspace. Choose different values for β. As decreases the phase R βr transitions become stronger. Study the phase diagram in terms of β g and β h
32 Order Parameters 4D (or space) plaquette) : extra dimension (or transverse) plaquette : 4D (or space) link: extra dimension (or transverse) link : Higgs field measure squared: P S P 6N 4N x, µ < ν 4 x, µ 4 cos (F cos (F µν µ (x)) (x)) L S cos (χ(x µˆ) A + + µˆ 4N x, µ 4 L cos (χ(x ˆ) A + + N x, µ 4 R = ρ (x) N x ˆ - χ(x)) - χ(x)) [ define: ϕ = ρ(x) exp(iχ (x)) ] L
33 The Phase Diagram β = 0. β = 0. β R g h = 0.00 C: Confining phase D Coulomb phase H : five dimensional Higgs phase H 4 : four dimensional Higgs phase broken symmetry on 4D subspace confinement along the extra dim
34 Confining - H 4 phase transition β = 0. β = g g 0. P does not feel the phase transition It remains in the confined regime The same happens to L R passes from a value ~ (unbroken) to values > (broken phase)
35 Confining-H phase transition β = 0. 8 β 0. = g g Both P and P S do feel the phase transition R passes from a value ~ (unbroken) to values > (broken phase) Big hysteresis loop: st order PT
36 Interesting features of the D Abelian-Higgs model with anisotropic couplings There is a stable phase with broken symmetry on the four-dimensional subspace and confinement along the extra-fifth dimension. Strong evidence can be provided that for a certain value of the scalar self-coupling (β R =0. () ) the transition from the strongly coupled phase to the layer Higgs phase becomes nd order. The separation of H 4 from the H phase seems to be a crossover (for a definite conclusion bigger volumes are needed)
37 (4+)-dimensional SU()- Higgs model in the adjoint representation
38 D SU()-Higgs in the adjoint representation It is a toy-model based on the Georgi-Glashow model The SU() symmetry breaks to U() massless photon massive W-bosons massive scalar neutral field In the Higgs phase The 3D model is equivalent with the SU() pure model at finite temperature after dimensional reduction due to the integration of the heavy modes It presents two phases (confining + Higgs) [ Hart, Philipsen, Stack and Teper Phys.Lett.B 997 ] A first numerical study of the 4D model can be found in [ Mitrjushkin and Zadorozhny, Phys.Lett.B 986 ]
39 The lattice model The action is : S D Lattice + β h + β h = β x,µ x + ( β g x, µ < ν 4 R Tr Tr 4β + [ Φ (x)] Tr[ Φ(x)U (x) Φ(x + µ)u (x)] + [ Φ (x)] Tr[ Φ(x)U ] (x)φ (x + ˆ)U (x) h β ) h x TrU µν Tr (x) + β g µ x,µ [ ] [ ] Φ (x) + β Tr Φ (x) R x TrU µ µ (x) The Links are defined by: U = iga µ iga µ = e U e The gauge potential and the matter fields are represented by x Hermitian matrices: a Aµ = Aµ σa and Φ = Φ a σ a (σ a : Pauli matrices) Five couplings: β, β, β, β g g h h and β R
40 Order Parameters 4D (or space) plaquette) : P S 6N x, µ < ν 4 TrU µν (x) extra dimension (or transverse) plaquette : P 4N x, µ 4 TrU µ (x) 4D (or space) link: L S = 4N x, µ 4 Tr + [ Φ(x)U (x)φx) + µ)u (x)]/ Tr[ Φ (x)] µ µ extra dimension (or transverse) link : + [ Φ(x)U + ] [ ] (x)φx) ˆ)U (x) / Tr Φ L = Tr (x) N x Higgs field measure squared: R = N x Tr [ Φ (x)]
41 The phase diagram of the model with isotropic couplings Take: βg = β g, βh = β h The phase diagram in the parametric-space of β g and β h for β R =0.0 is: New Higgs phases of the D model H S : five dimensional Higgs phase with the U() symmetry in the confining regime H C : five dimensional Higgs phase with the U() symmetry in the Coulomb regime The pure SU() transition point, β g ~.63 [ Creutz, Phys.Rev.Lett. 979 ]
42 Relationship of the Layer phase and the dimensionality A lattice model defined in D=d+n dimensions can provide a Layer phase as long as the d-dimensional model can be found in at least two phases one of which is the Coulomb phase. Fu and Nielsen NPB 984, 98 Therefore it is reasonable that a 4D layer phase can exist in the D anisotropic U() gauge model since the phase diagram of the four-dimensional model consists of two phases : confining and Coulomb. On the contrary, the D anisotropic SU() gauge model can not furnish a layer phase since it is known that the 4D SU() gauge model does not have a well defined Coulomb phase. However it can exist a D layer phase of SU() in a 6D space. But, what does it happen when the scalar field is added?
43 The phase diagram of the model with anisotropic couplings For β = 0 and β = 0 g h the model becomes four-dimensional. It has a confining phase (for β h small) and a four-dimensional Higgs phase (for β h big). The U() symmetry that survives in the Higgs phase shows a phase transition between the strong coupled and the weak phase (following the β value). g The parameter β R controls the strength of the phase transitions Switch on β and : β g β h Keep h small (=0.0). Vary β g in the interval for which the confined phase can be present (β g <.63). Give the Phase Diagram in terms of β h and β g
44 SU() Confining phase The Phase Diagram β g =. D Coulomb phase (for SU()) H : five dimensional Higgs phase U() unbroken in D H 4 : four dimensional Higgs phase U() unbroken in 4D space SU() confinement along the extra dim
45 H 4 H phase transition β g =. P S ~-(/4β g ) P S ~-(/β g ) & P S ~ P P ~β g /4 Restoration of the D dynamics in the Higgs phase L ~small For both H 4 and H the order parameter R >> O()
46 Confining - H 4 phase transition β g =.
47 Confining - H phase transition β g =.
48 The Higgs phase H 4 is located in a four-dimensional subspace embedded in a five-dimensional space. A massless photon is found to be localized on the four-dimensional subspace The confinement along the extra dimension due to the SU() interaction serves for the screening of the extra dimension. H 4 is a four-dimensional Layer phase formed in a five-dimensional bulk It shares the characteristics of the analytical solution of the Dvali-Shifman model (Phys.Lett.B 997) for the localisation of a massless photon on a two-dimensional wall out of which the interaciton is confined by the SU() interaction.
49 Remarks & Conclusions (D+)-dimensional gauge models with anisotropic couplings can reveal a new kind of D-dimensional phase which we call Layer. It is a D-dimensional Coulomb phase accompanied by confinement along the extra dimension. The necessary condition for the layer phase formation is that the D-dimensional gauge model must already have two distinct phases. Hence the minimum dimensionality is D=4 for the pure U() model and D= for the pure SU() model. Extra dimensional lattice gauge models with anisotropic couplings can be inspired in an extra dimensional space described by the RS metric.
50 The study of the D-Abelian Higgs model with anisotropic couplings shows that a Layer phase exists in the broken phase: we get a set of 4-dimensional subspaces in the Higgs phase which do not comunicate due to confinement along the extra direction. The D anisotropic SU()-Higgs model in the adjoint representation shows two main features: The inclusion of the scalar field is responsible for the formation of a 4 dimensional layer (higgs) phase in a model with non-abelian dynamics The confinement along the extra dimension is of the non-abelian type The existence of the layer phase in the phase diagram of (4+)D lattice gauge models with anisotropic couplings supports the conjecture of an effectively four-dimensional world embedded in a bulk of extra dimensions.
Numerical study of stable classical solutions of Quantum Field Theory
THALES Project No. 65/1320 Numerical study of stable classical solutions of Quantum Field Theory RESEARCH TEAM: G.Koutsoumbas, Assoc. Professor, NTUA K.Farakos, Assoc. Professor, NTUA N.D.Tracas, Assoc.
More informationSTABILIZING EXTRA DIMENSIONS
STABILIZING EXTRA DIMENSIONS Gero von Gersdorff (École Polytechnique) Warsaw, October 19th 2009 Collaboration with J.A.Cabrer and M.Quirós OUTLINE Features of Warped Extra Dimensions Stabilizing Models
More informationLarge Extra Dimensions and the Hierarchy Problem
Large Extra Dimensions and the Hierarchy Problem The Hierarchy Problem - At Planck energies (M P L 10 19 GeV ) all four forces have the same strength. -At the Electroweak scale (M EW 1T ev ) the four forces
More informationBrane world scenarios
PRAMANA cfl Indian Academy of Sciences Vol. 60, No. 2 journal of February 2003 physics pp. 183 188 Brane world scenarios DILEEP P JATKAR Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad
More informationBraneworlds: gravity & cosmology. David Langlois APC & IAP, Paris
Braneworlds: gravity & cosmology David Langlois APC & IAP, Paris Outline Introduction Extra dimensions and gravity Large (flat) extra dimensions Warped extra dimensions Homogeneous brane cosmology Brane
More informationElementary/Composite Mixing in Randall-Sundrum Models
Elementary/Composite Mixing in Randall-Sundrum Models Brian Batell University of Minnesota with Tony Gherghetta - arxiv:0706.0890 - arxiv:0710.1838 Cornell 1/30/08 5D Warped Dimension = 4D Strong Dynamics
More informationIntroduction to (Large) Extra Dimensions
SLAC Dark Matter & Exotic Physics WG p. 1/39 Introduction to (Large) Extra Dimensions A. Lionetto Department of Physics & INFN Roma Tor Vergata SLAC Dark Matter & Exotic Physics WG p. 2/39 Outline Introduction
More information1. Introduction. [Arkani-Hamed, Dimopoulos, Dvali]
2014 Ï Ò (í «) Ò Ò Ù Åǽ À 20145 7 Content 1. Introduction and Motivation 2. f(r)-brane model and solutions 3. Localization of gravity on f(r)-brane 4. Gravity resonances on f(r)-brane 5. Corrections to
More informationELECTROWEAK BREAKING IN EXTRA DIMENSIONS MINI REVIEW. Gero von Gersdorff (École Polytechnique) Moriond Electroweak Session, La Thuile, March 2011
ELECTROWEAK BREAKING IN EXTRA DIMENSIONS MINI REVIEW Gero von Gersdorff (École Polytechnique) Moriond Electroweak Session, La Thuile, March 2011 OUTLINE How can Extra Dimensions explain the electroweak
More informationWarped Models in String Theory
Warped Models in String Theory SISSA/ISAS Trieste (Italy) Rutgers 14 November 2006 (Work in collaboration with B.S.Acharya and F.Benini) Appearing soon Introduction 5D Models 5D warped models in a slice
More informationarxiv:hep-th/ v1 28 Apr 2002
Vector field localization and negative tension branes Massimo Giovannini Institute of Theoretical Physics, University of Lausanne BSP-1015 Dorigny, Lausanne, Switzerland arxiv:hep-th/0204235v1 28 Apr 2002
More informationExotic Dark Matter as Spin-off of Proton Stability. Kaustubh Agashe (University of Maryland)
Exotic Dark Matter as Spin-off of Proton Stability Kaustubh Agashe (University of Maryland) Outline and Summary Warped extra dimensions address Planckweak and flavor hierarchies: new (KK) particles at
More informationWarp Duality in Braneworlds
Warp Duality in Braneworlds Andrew B. McGowan September 14, 2007 Abstract In recent years there have emerged numerous models of spacetime that include extra dimensions. In particular there have been a
More informationINTRODUCTION TO EXTRA DIMENSIONS
INTRODUCTION TO EXTRA DIMENSIONS MARIANO QUIROS, ICREA/IFAE MORIOND 2006 INTRODUCTION TO EXTRA DIMENSIONS p.1/36 OUTLINE Introduction Where do extra dimensions come from? Strings and Branes Experimental
More informationScalar field dark matter and the Higgs field
Scalar field dark matter and the Higgs field Catarina M. Cosme in collaboration with João Rosa and Orfeu Bertolami Phys. Lett., B759:1-8, 2016 COSMO-17, Paris Diderot University, 29 August 2017 Outline
More informationThick Brane World. Seyen Kouwn Korea Astronomy and Space Science Institute Korea
Thick Brane World Seyen Kouwn Korea Astronomy and Space Science Institute Korea Introduction - Multidimensional theory 1 Why are the physically observed dimensions of our Universe = 3 + 1 (space + time)?
More information...and the extradimensions quest
A brief introduction to the Randall-Sundrum Models...and the extradimensions quest Bruno BERTRAND Center for particle physics and phenomenology (CP3) CP3 Seminar : Randall-Sundrum models - Bruno BERTRAND
More informationIntroduction to AdS/CFT
Introduction to AdS/CFT D-branes Type IIA string theory: Dp-branes p even (0,2,4,6,8) Type IIB string theory: Dp-branes p odd (1,3,5,7,9) 10D Type IIB two parallel D3-branes low-energy effective description:
More informationLOCALIZATION OF FIELDS ON A BRANE IN SIX DIMENSIONS.
LOCALIZATION OF FIELDS ON A BRANE IN SIX DIMENSIONS Merab Gogberashvili a and Paul Midodashvili b a Andronikashvili Institute of Physics, 6 Tamarashvili Str., Tbilisi 3877, Georgia E-mail: gogber@hotmail.com
More informationAharonov-Bohm Effect and Unification of Elementary Particles. Yutaka Hosotani, Osaka University Warsaw, May 2006
Aharonov-Bohm Effect and Unification of Elementary Particles Yutaka Hosotani, Osaka University Warsaw, May 26 - Part 1 - Aharonov-Bohm effect Aharonov-Bohm Effect! B)! Fµν = (E, vs empty or vacuum!= Fµν
More informationBrane Gravity from Bulk Vector Field
Brane Gravity from Bulk Vector Field Merab Gogberashvili Andronikashvili Institute of Physics, 6 Tamarashvili Str., Tbilisi 380077, Georgia E-mail: gogber@hotmail.com September 7, 00 Abstract It is shown
More informationModelling an extra dimension with domain-wall branes
Modelling an extra dimension with domain-wall branes Damien George Nikhef theory seminar 5 th November 2009 Overview Physics beyond the standard model: extra dimensions. Brane domain wall (topological
More informationLife with More Than 4: Extra Dimensions
Life with More Than 4: Extra Dimensions Andrew Larkoski 4/15/09 Andrew Larkoski SASS 5 Outline A Simple Example: The 2D Infinite Square Well Describing Arbitrary Dimensional Spacetime Motivations for Extra
More informationSearching for Extra Space Dimensions at the LHC. M.A.Parker Cavendish Laboratory Cambridge
Searching for Extra Space Dimensions at the LHC M.A.Parker Cavendish Laboratory Cambridge I shall use ATLAS to illustrate LHC physics, because it is the experiment I know best. Both general purpose detectors
More informationGauge coupling unification without leptoquarks Mikhail Shaposhnikov
Gauge coupling unification without leptoquarks Mikhail Shaposhnikov March 9, 2017 Work with Georgios Karananas, 1703.02964 Heidelberg, March 9, 2017 p. 1 Outline Motivation Gauge coupling unification without
More informationD. f(r) gravity. φ = 1 + f R (R). (48)
5 D. f(r) gravity f(r) gravity is the first modified gravity model proposed as an alternative explanation for the accelerated expansion of the Universe [9]. We write the gravitational action as S = d 4
More informationIntroduction to the Beyond the Standard Model session
Introduction to the Beyond the Standard Model session JJC 2014 Dec. 11th 2014 Samuel Calvet Outline Why do we need Beyond the Standard Model (BSM) theories? BSM theories on the market : their predictions/particles
More informationNumerical Solutions in 5D Standing Wave Braneworld
Numerical Solutions in 5D Standing Wave Braneworld Merab Gogberashvili 1,2, Otari Sakhelashvili 1, and Giorgi Tukhashvili 1 arxiv:1304.6079v1 [hep-th] 22 Apr 2013 1 I. Javakhishvili Tbilisi State University,
More informationMagnetic moment (g 2) µ and new physics
Dresden Lepton Moments, July 2010 Introduction A 3σ deviation for a exp µ a SM µ has been established! Currently: a exp µ a SM µ = (255 ± 63 ± 49) 10 11 Expected with new Fermilab exp. (and th. progress):
More informationIntroduction to Black Holes, Extra Dimensions and Colliders
Introduction to Black Holes, Extra Dimensions and Colliders James Frost Institute of Physics Half-day Meeting Thursday 9th December 2010 James Frost (University of Cambridge) IOP Half-Day Meeting Thursday
More informationGauge Field Localization in Models with Large Extra Dimensions
Gauge Field Localization in Models with Large Extra Dimensions Norisuke Sakai (Tokyo Woman s Christian University) In collaboration with Kazutoshi Ohta, Progress of Theoretical Physics 124, 71 (2010) [arxiv:1004.4078],talk
More informationGauge-Higgs Unification on Flat Space Revised
Outline Gauge-Higgs Unification on Flat Space Revised Giuliano Panico ISAS-SISSA Trieste, Italy The 14th International Conference on Supersymmetry and the Unification of Fundamental Interactions Irvine,
More informationInter-brane distance stabilization by bulk Higgs field in RS model
EPJ Web of Conferences 58, 0500 07 QFTHEP 07 DOI: 0.05/epjconf/07580500 Inter-brane distance stabilization by bulk Higgs field in RS model Vadim Egorov,, and Igor Volobuev, Skobeltsyn Institute of Nuclear
More informationProgress in Gauge-Higgs Unification on the Lattice
Progress in Gauge-Higgs Unification on the Lattice Kyoko Yoneyama (Wuppertal University) in collaboration with Francesco Knechtli(Wuppertal University) ikos Irges(ational Technical University of Athens)
More informationBraneworld in f(r) gravity and critical gravity
Braneworld in f(r) gravity and critical gravity Yu-Xiao Liu Institute of Theoretical Physics, Lanzhou University ICTS, USTC, Hefei 2011.12.13 Content Introduction and motivation f(r) thick brane f(r) thick
More informationExploring Universal Extra-Dimensions at the LHC
Exploring Universal Extra-Dimensions at the LHC Southampton University & Rutherford Appleton Laboratory 1 Problems to be addressed by the underlying theory The Nature of Electroweak Symmetry Breaking The
More informationTheories with Compact Extra Dimensions
Instituto de Física USP PASI 2012 UBA Theories with Compact Extra dimensions Part II Generating Large Hierarchies with ED Theories Warped Extra Dimensions Warped Extra Dimensions One compact extra dimension.
More informationCosmology and astrophysics of extra dimensions
Cosmology and astrophysics of extra dimensions Astrophysical tests of fundamental physics Porto, 27-29 March 2007 P. Binétruy, APC Paris Why extra dimensions? Often appear in the context of unifying gravitation
More informationSolutions to gauge hierarchy problem. SS 10, Uli Haisch
Solutions to gauge hierarchy problem SS 10, Uli Haisch 1 Quantum instability of Higgs mass So far we considered only at RGE of Higgs quartic coupling (dimensionless parameter). Higgs mass has a totally
More informationCOSMOLOGY IN HIGHER DIMENSIONS
COSMOLOGY IN HIGHER DIMENSIONS 1. Introduction 2. Overview of Higher Dimensional Cosmology 3. Cosmology in Higher Dimensions 4. String Frame 5. Summary Kei-ichi MAEDA Waseda University 1. INTRODUCTION
More informationFLAVOUR IN WARPED EXTRA DIMENSIONS
FLAVOUR IN WARPED EXTRA DIMENSIONS G. CACCIAPAGLIA Institut de Physique Nucléaire de Lyon, Université Lyon, CNRS/IN2P3, F-69622 Villeurbanne Cedex, France Models in warped extra dimensions are very attractive
More informationAccidental SUSY at the LHC
Accidental SUSY at the LHC Tony Gherghetta (University of Melbourne) PACIFIC 2011, Moorea, French Polynesia, September 12, 2011 with Benedict von Harling and Nick Setzer [arxiv:1104.3171] 1 What is the
More informationGravity in the Braneworld and
Gravity in the Braneworld and the AdS/CFT Correspondence Takahiro TANAKA Department of Physics, Kyoto University, Kyoto 606-8502, Japan October 18, 2004 Abstract We discuss gravitational interaction realized
More informationIntroduction to the Beyond the Standard Model session
Introduction to the Beyond the Standard Model session JRJC 2015 Nov. 19th 2015 Samuel Calvet Outline Why do we need Beyond the Standard Model (BSM) theories? BSM theories on the market : their predictions/particles
More informationProgress in Gauge-Higgs Unification on the Lattice
Progress in Gauge-Higgs Unification on the Lattice Francesco Knechtli, Kyoko Yoneyama, Peter Dziennik Department of Physics, Bergische Universität Wuppertal Gaussstr., D-49 Wuppertal, Germany E-mail: knechtli@physik.uni-wuppertal.de,
More informationA framework for domain-wall brane model building
A framework for domain-wall brane model building Raymond R. Volkas The University of Melbourne Beyond the Standard Models of Particle Physics, Cosmology and Astrophysics Feb 2010 Raymond R. Volkas (U Melbourne)
More informationPhysics Beyond the Standard Model. Marina Cobal Fisica Sperimentale Nucleare e Sub-Nucleare
Physics Beyond the Standard Model Marina Cobal Fisica Sperimentale Nucleare e Sub-Nucleare Increasingly General Theories Grand Unified Theories of electroweak and strong interactions Supersymmetry
More informationLarge Mass Hierarchy from a Small Extra Dimension
Large Mass Hierarchy from a Small Extra Dimension Sridip Pal (09MS002) DPS PH4204 April 4,2013 Sridip Pal (09MS002) DPS PH4204 () Large Mass Hierarchy from a Small Extra Dimension April 4,2013 1 / 26 Outline
More informationBeyond the Standard Model
4 KIT, 6-10 February 12 Beyond the Standard Model Guido Altarelli Universita di Roma Tre CERN Solutions to the hierarchy problem Supersymmetry: boson-fermion symm. The most ambitious and widely accepted
More informationBeyond the standard model searches at the Tevatron
Beyond the standard model searches at the Tevatron G. Sajot To cite this version: G. Sajot. Beyond the standard model searches at the Tevatron. 3th International Symposium on Particles, Strings and Cosmology
More informationStrings, gauge theory and gravity. Storrs, Feb. 07
Strings, gauge theory and gravity Storrs, Feb. 07 Outline Motivation - why study quantum gravity? Intro to strings Gravity / gauge theory duality Gravity => gauge: Wilson lines, confinement Gauge => gravity:
More informationBEYOND THE SM (II) Kaustubh Agashe (University of Maryland)
BEYOND THE SM (II) Kaustubh Agashe (University of Maryland) ierarchy problems (from lecture 1) Planck-weak hierarchy problem Flavor (hierarchy) puzzle...extra dimensions can address both... Extra dimensions:
More informationTime-Like Extra Dimension and Cosmological Constant in Brane Models. Tianjun Li
UPR-901-T Time-Like Extra Dimension and Cosmological Constant in Brane Models Tianjun Li Department of Physics and Astronomy University of Pennsylvania, Philadelphia, PA 19104-6396 U. S. A. Abstract We
More informationGauge field localization on brane worlds
Gauge field localization on brane worlds Rommel Guerrero and R. Omar Rodriguez Universidad Centroccidental Lisandro Alvarado - Venezuela Miami 2013 R. Guerrero UCLA) Gauge field localization December 2013
More informationDoes a Randall-Sundrum scenario create the illusion of a torsion-free universe?
hep-th/0204242 Does a Randall-Sundrum scenario create the illusion of a torsion-free universe? Biswarup Mukhopadhyaya 1, Somasri Sen 2 Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad
More informationCURRICULUM VITAE. Personal Data Name Farakos Konstantinos Place of birth Greece
CURRICULUM VITAE Personal Data Name Farakos Konstantinos Place of birth Greece Studies and position -University of Athens, 1974-1979 (Bachelor in Physics) -NRC Democritos, 1979-1981 (Theoretical Physics
More informationA non-perturbative view of the Higgs hierarchy problem
A non-perturbative view of the Higgs hierarchy problem Corfu Workshop on SM and Beyond, 31 Aug. - 11 Sept. 2013 Nikos Irges National Technical University of Athens Based on N.I. and F. Knechtli Nucl. Phys.
More informationPoS(Kruger 2010)034. CMS searches for new physics. Mara Senghi Soares On behalf of the CMS Collaboration.
On behalf of the CMS Collaboration E-mail: mara.senghi@ciemat.es We discuss the first searches for new physics being carried out with the CMS detector, at the early stage of data taking. Prospects for
More informationG2 gauge theories. Axel Maas. 14 th of November 2013 Strongly-Interacting Field Theories III Jena, Germany
G2 gauge theories Axel Maas 14 th of November 2013 Strongly-Interacting Field Theories III Jena, Germany Overview Why G2? Overview Why G2? G2 Yang-Mills theory Running coupling [Olejnik, Maas JHEP'08,
More informationExtra Dimensional Signatures at CLIC
Extra Dimensional Signatures at CLIC Thomas G. Rizzo SLAC A brief overview is presented of the signatures for several different models with extra dimensions at CLIC, an e + e linear collider with a center
More informationPHY 396 K. Problem set #11, the last set this semester! Due December 1, 2016.
PHY 396 K. Problem set #11, the last set this semester! Due December 1, 2016. In my notations, the A µ and their components A a µ are the canonically normalized vector fields, while the A µ = ga µ and
More informationGravitational perturbations on branes
º ( Ò Ò ) Ò ± 2015.4.9 Content 1. Introduction and Motivation 2. Braneworld solutions in various gravities 2.1 General relativity 2.2 Scalar-tensor gravity 2.3 f(r) gravity 3. Gravitational perturbation
More informationAdS/CFT duality. Agnese Bissi. March 26, Fundamental Problems in Quantum Physics Erice. Mathematical Institute University of Oxford
AdS/CFT duality Agnese Bissi Mathematical Institute University of Oxford March 26, 2015 Fundamental Problems in Quantum Physics Erice What is it about? AdS=Anti de Sitter Maximally symmetric solution of
More informationEXOTICA AT LHC. Philippe Miné LPNHE-Ecole Polytechnique, IN2P3-CNRS, France CMS collaboration.
EXOTICA AT LHC Philippe Miné LPNHE-Ecole Polytechnique, IN2P3-CNRS, France CMS collaboration pmine@poly.in2p3.fr Chia, Sardinia, Italy October 24-27 2001 1 EXOTICA AT LHC Beyond the Standard Model, Supersymmetry
More informationEffective theories for QCD at finite temperature and density from strong coupling
XQCD 2011 San Carlos, July 2011 Effective theories for QCD at finite temperature and density from strong coupling Owe Philipsen Introduction to strong coupling expansions SCE for finite temperature: free
More informationNon-SUSY BSM: Lecture 1/2
Non-SUSY BSM: Lecture 1/2 Generalities Benasque September 26, 2013 Mariano Quirós ICREA/IFAE Mariano Quirós (ICREA/IFAE) Non-SUSY BSM: Lecture 1/2 1 / 31 Introduction Introduction There are a number of
More informationt Hooft-Polyakov Monopoles on the Lattice
t Hooft-Polyakov Monopoles on the Lattice Davis,Kibble,Rajantie&Shanahan, JHEP11(2000) Davis,Hart,Kibble&Rajantie, PRD65(2002) Rajantie, in progress 19 May 2005 University of Wales, Swansea Introduction
More informationDeconstructing six dimensional gauge theories with strongly coupled moose meshes
HUTP-02/A031 hep-ph/0207164 Deconstructing six dimensional gauge theories with strongly coupled moose meshes Thomas Gregoire and Jay G. Wacker Department of Physics, University of California Berkeley,
More informationYet Another Alternative to Compactification
Okayama Institute for Quantum Physics: June 26, 2009 Yet Another Alternative to Compactification Heterotic five-branes explain why three generations in Nature arxiv: 0905.2185 [hep-th] Tetsuji KIMURA (KEK)
More informationSearch for Randall-Sundrum Gravitons and Intermediate-Mass Diphoton Resonances
Search for Randall-Sundrum Gravitons and Intermediate-Mass Diphoton Resonances (CMS Draft Analysis Note) V. Litvin, H. Newman, T. Orimoto, E. Schneider California Institute of Technology, Pasadena, CA,
More informationS = 2 decay in Warped Extra Dimensions
S = 2 decay in Warped Extra Dimensions Faisal Munir IHEP, Beijing Supervisor: Cai-Dian Lü HFCPV CCNU, Wuhan October 28, 2017 based on: Chin. Phys. C41 (2017) 053106 [arxiv:1607.07713] F. Munir (IHEP) New
More informationarxiv: v3 [hep-ph] 22 Dec 2017
SLAC PUB 17154 September, 2017 arxiv:1709.07909v3 [hep-ph] 22 Dec 2017 Competing Forces in 5-Dimensional Fermion Condensation Jongmin Yoon and Michael E. Peskin 1 SLAC, Stanford University, Menlo Park,
More informationGauge theories on a five-dimensional orbifold
arxiv:hep-lat/0509071v1 21 Sep 2005 and Burkhard Bunk Institut für Physik, Humboldt Universität, Newtonstr. 15, 12489 Berlin, Germany E-mail: knechtli@physik.hu-berlin.de, bunk@physik.hu-berlin.de Nikos
More information125 GeV Higgs Boson and Gauge Higgs Unification
125 GeV Higgs Boson and Gauge Higgs Unification Nobuchika Okada The University of Alabama Miami 2013, Fort Lauderdale, Dec. 12 18, 2013 Discovery of Higgs boson at LHC! 7/04/2012 Standard Model Higgs boson
More information4D Gravity on a Brane in 5D Minkowski Space
NYU-TH/00/04/0 April 25, 2000 4D Gravity on a Brane in 5D Minkowski Space Gia Dvali, Gregory Gabadadze, Massimo Porrati Department of Physics, New York University, New York, NY 0003 Abstract We suggest
More informationString Phenomenology ???
String Phenomenology Andre Lukas Oxford, Theoretical Physics d=11 SUGRA IIB M IIA??? I E x E 8 8 SO(32) Outline A (very) basic introduction to string theory String theory and the real world? Recent work
More informationNucleons from 5D Skyrmions
Nucleons from 5D Skyrmions Giuliano Panico Physikalisches Institut der Universität Bonn Planck 2009 26 May 2009 Based on G. P. and A. Wulzer 0811.2211 [hep-ph] and A. Pomarol and A. Wulzer 0807.0316 [hep-ph]
More informationIntroduction to String Theory ETH Zurich, HS11. 9 String Backgrounds
Introduction to String Theory ETH Zurich, HS11 Chapter 9 Prof. N. Beisert 9 String Backgrounds Have seen that string spectrum contains graviton. Graviton interacts according to laws of General Relativity.
More informationFuzzy extra dimensions and particle physics models
Fuzzy extra dimensions and particle physics models Athanasios Chatzistavrakidis Joint work with H.Steinacker and G.Zoupanos arxiv:1002.2606 [hep-th] Corfu, September 2010 Overview Motivation N = 4 SYM
More informationsolving the hierarchy problem Joseph Lykken Fermilab/U. Chicago
solving the hierarchy problem Joseph Lykken Fermilab/U. Chicago puzzle of the day: why is gravity so weak? answer: because there are large or warped extra dimensions about to be discovered at colliders
More informationYet Another Alternative to Compactification by Heterotic Five-branes
The University of Tokyo, Hongo: October 26, 2009 Yet Another Alternative to Compactification by Heterotic Five-branes arxiv: 0905.285 [hep-th] Tetsuji KIMURA (KEK) Shun ya Mizoguchi (KEK, SOKENDAI) Introduction
More informationThe Higgs Mechanism and the Higgs Particle
The Higgs Mechanism and the Higgs Particle Heavy-Ion Seminar... or the Anderson-Higgs-Brout-Englert-Guralnik-Hagen-Kibble Mechanism Philip W. Anderson Peter W. Higgs Tom W. B. Gerald Carl R. François Robert
More informationNatural Inflation and Quantum Gravity
Natural Inflation and Quantum Gravity Raman Sundrum University of Maryland Based on arxiv:1412.3457 (to appear in PRL) with Anton de la Fuente and Prashant Saraswat 1 Natural Inflation and Quantum Gravity
More informationParticles and Strings Probing the Structure of Matter and Space-Time
Particles and Strings Probing the Structure of Matter and Space-Time University Hamburg DPG-Jahrestagung, Berlin, March 2005 2 Physics in the 20 th century Quantum Theory (QT) Planck, Bohr, Heisenberg,...
More informationAether compactification
PHYSICAL REVIEW D 78, 044047 (2008) Aether compactification Sean M. Carroll 1 and Heywood Tam 1 1 California Institute of Technology, Pasadena, California 91125, USA (Received 8 April 2008; published 29
More informationarxiv:quant-ph/ v1 16 Jun 2005
Black-body radiation in extra dimensions Haavard Alnes, Finn Ravndal 2 and Ingunn Kathrine Wehus 3 Institute of Physics, University of Oslo, N-036 Oslo, Norway. arxiv:quant-ph/05063 v 6 Jun 2005 Abstract
More informationThe Randall-Sundrum model
The Randall-Sundrum model Aleksandr Chatrchyan & Björn Jüliger After a brief non-technical introduction to the Hierarchy problem, we first discuss the old five-dimensional Kaluza-Klein model, its tower
More informationTowards particle physics models from fuzzy extra dimensions
Towards particle physics models from fuzzy extra dimensions Athanasios Chatzistavrakidis National Technical University and NCSR Demokritos, Athens Joint work with H.Steinacker and G.Zoupanos Particles
More informationLepton flavour violation in RS models
Lepton flavour violation in RS models P. Moch with M. Beneke and J. Rohrwild Theoretische Physik 1 Uni Siegen Outline: Introduction Strategy and formalism Results P. Moch (Uni Siegen LVF in RS PSI, Oktober
More informationAxion in Large Extra Dimensions
Axion in Large Extra Dimensions Talk at ASK2011 Sanghyeon Chang Konkuk Univ. April 11, 2011 Sanghyeon Chang (Konkuk Univ.) Axion in Large Extra Dimensions April 11, 2011 1 / 27 Table of Contents 1 Introduction
More information10 Interlude: Preview of the AdS/CFT correspondence
10 Interlude: Preview of the AdS/CFT correspondence The rest of this course is, roughly speaking, on the AdS/CFT correspondence, also known as holography or gauge/gravity duality or various permutations
More informationNonlinear massive gravity and Cosmology
Nonlinear massive gravity and Cosmology Shinji Mukohyama (Kavli IPMU, U of Tokyo) Based on collaboration with Antonio DeFelice, Emir Gumrukcuoglu, Chunshan Lin Why alternative gravity theories? Inflation
More informationThe Correct Interpretation of the Kaluza-Klein Theory
Copyright 2014 by Sylwester Kornowski All rights reserved The Correct Interpretation of the Kaluza-Klein Theory Sylwester Kornowski Abstract: Here, within the Scale-Symmetric Everlasting Theory (S-SET),
More informationSupersymmetric Randall-Sundrum Scenario
CIT-USC/00-015 Supersymmetric Randall-Sundrum Scenario arxiv:hep-th/000117v May 000 Richard Altendorfer, Jonathan Bagger Department of Physics and Astronomy The Johns Hopkins University 400 North Charles
More informationGeneral Warped Solution in 6d Supergravity. Christoph Lüdeling
General Warped Solution in 6d Supergravity Christoph Lüdeling DESY Hamburg DPG-Frühjahrstagung Teilchenphysik H. M. Lee, CL, JHEP 01(2006) 062 [arxiv:hep-th/0510026] C. Lüdeling (DESY Hamburg) Warped 6d
More informationDuality and Holography
Duality and Holography? Joseph Polchinski UC Davis, 5/16/11 Which of these interactions doesn t belong? a) Electromagnetism b) Weak nuclear c) Strong nuclear d) a) Electromagnetism b) Weak nuclear c) Strong
More informationHUGS Dualities and QCD. Josh Erlich LECTURE 5
HUGS 2012 Dualities and QCD Josh Erlich LECTURE 5 Outline The meaning of duality in physics (Example: The Ising model) Quark-Hadron duality (experimental and theoretical evidence) Electric-Magnetic Duality
More informationThe Higgs boson. as a window to Beyond the Standard Model Physics. Roberto Contino. Università di Roma La Sapienza
The Higgs boson as a window to Beyond the Standard Model Physics Roberto Contino Università di Roma La Sapienza 1. what have we discovered so far...... and why we need an EWSB sector The physics discovered
More informationNTNU Trondheim, Institutt for fysikk
NTNU Trondheim, Institutt for fysikk Examination for FY3464 Quantum Field Theory I Contact: Michael Kachelrieß, tel. 99890701 Allowed tools: mathematical tables Some formulas can be found on p.2. 1. Concepts.
More informationCenter-symmetric dimensional reduction of hot Yang-Mills theory
Center-symmetric dimensional reduction of hot Yang-Mills theory Institut für Theoretische Physik, ETH Zürich, CH-809 Zürich, Switzerland E-mail: kurkela@phys.ethz.ch It is expected that incorporating the
More information