Aspects of Spontaneous Lorentz Violation
|
|
- Lesley Skinner
- 5 years ago
- Views:
Transcription
1 Aspects of Spontaneous Lorentz Violation Robert Bluhm Colby College IUCSS School on CPT & Lorentz Violating SME, Indiana University, June 2012
2 Outline: I. Review & Motivations II. Spontaneous Lorentz Violation III. Nambu-Goldstone Modes & Higgs Mech. IV. Examples: Bumblebee & Tensor Models V. Conclusions
3 I. Review & Motivations Lorentz symmetry comes in two varieties: global local symmetry of special relativity - field theories invariant under global LTs symmetry of general relativity - Lorentz symmetry holds locally Previous talk looked at how to construct the SME in the presence of gravity SME lagrangian observer scalar formed from tensors, covariant derivatives, spinors, gamma matrices, etc. & SME coeffs.
4 SME with Gravity includes gravity, SM, and LV sectors Have 2 symmetries in gravity: local Lorentz symmetry spacetime diffeomorphisms GR involves tensors on a curved spacetime manifold T λµν... spacetime tensor components To reveal the local Lorentz symmetry, introduce local tensor components in Lorentz frames T abc... local Lorentz frame components
5 These components are connected by a vierbein vierbein: relates local and manifold frames tetrad of spacetime coord. vectors can accommodate spinors In a vierbein formalism, must also introduce a spin connection spin connection: appears in cov. derivs. of local tensors In Riemann spacetime with (metric) spin connection is determined by the vierbein not independent degrees of freedom
6 Can also introduce torsion T λ µν = Γ λ µν - Γ λ νµ spin connection becomes dynamically independent gives gravity the form of a gauge theory 16 components 24 components New geometry emerges: Riemann-Cartan spacetime curvature = R κ λµν torsion = T λ µν no evidence for (or against) torsion but should exist if gravity is like a gauge theory The SME with gravity includes curvature & torsion
7 Constructing the SME with Gravity Example: fermion coupled to gravity: where Additional fermion couplings might include:
8 Terms in the pure-gravity sector might include: For exploring phenomenology, it is useful to start with a minimal model that extends GR (without torsion) Riemannian limit (zero torsion): Jay Tasson s talk will look at phenomenology
9 Explicit vs. Spontaneous Lorentz Violation (SLV) SME coeffs. can result from either spontaneous or explicit Lorentz violation With explicit LV But with spontaneous LV No-go theorem: act as fixed background fields in any observer frame arise as vev s must be treated dynamically explicit breaking incompatible with geometrical identities, but spontaneous symmetry breaking evades this difficulty
10 Spontaneous Lorentz Violation (SLV) Question: What happens if Lorentz symmetry is spontaneously broken in a theory of gravity? originally motivated from quantum gravity & string theory Open Problem General Relativity is a classical theory not compatible with quantum physics Expect particle physics and classical gravity to merge in a quantum theory of gravity Planck scale: Is Lorentz symmetry exact at the Planck scale?
11 String Theory & SLV Mechanisms exist in SFT that could lead to vector/tensor fields acquiring nonzero vacuum expectation values (vevs) Nonpertubative vacuum in string field theory Produces vevs for tensor fields <Τ> 0 can lead to spontaneous Lorentz violation provides most elegant form of Lorentz violation fundamental theory fully Lorentz invariant vacuum breaks Lorentz symmetry evades the no-go theorem SME coeffs., e.g., a µ, b µ, c µν, d µν, H µν,... arise as vacuum expectation values when SLV occurs
12 II. Spontaneous Lorentz Violation A symmetry is spontaneously broken when the eqs. of motion obey the symmetry but the solutions do not. e.g., magnet dipole-dipole ints. are spatially symmetric but when a magnet forms the dipoles align along a particular direction The rotational symmetry is spontaneously broken e.g., push on a stick it s rotationally symmetric but it buckles in a spontaneously chosen direction in space With SSB, the symmetry is still there dynamically, but is hidden by the solution
13 Spontaneous symmetry breaking occurs in gauge theories e.g., in the electroweak theory, a scalar field has a vacuum solution (vev) that breaks the gauge symmetry a potential V has a nonzero minimum V The theory has multiple potential vacuum solutions f the physical vacuum picks one, breaking the symmetry
14 In the electroweak theory, the vev is a constant scalar has no preferred directions or rest frame preserves Lorentz symmetry But what if a vector or tensor field acquires a nonzero vev? there would be preferred directions in spacetime spontaneous breaking of Lorentz symmetry const. scalar field (electroweak) V <f> 0 f tensor vev <T> 0 vacuum breaks Lorentz symmetry
15 How is SLV introduced? Consider a Lorentz-invariant lagrangian L with tensor fields T include a potential that occurs when T V that has a nontrivial minimum has a nonzero vev T =0 e.g., in flat spacetime, with components T abc V = V (T abc ad be cf...t def t 2 ) has a minimum when T abc t abc = 0 where t 2 = t abc ad be cf...t def What about in curved spacetime? Lorentz symmetry is a local symmetry
16 Use a vierbein description in curved spacetime vierbein connects spacetime tensors to tensors in local Lorentz frame spacetime components e.g., local frame components allows spinors (fermions) to be introduced gives a structure like a local gauge theory also involves the spin connection appears in covariant derivs. of local tensors nondynamical in Riemann space (no torsion) dynamical in Riemann-Cartan space (torsion)
17 In curved spacetime, the Lagrangian is invariant under both local Lorentz transfs and diffeomorphisms b - rotations & boosts in local frame a = a b T abc T abc + d a T dbc + e b T aec + - spacetime diffeomorphisms x µ x µ + µ + b T µ... T µ... ( )T µ... ( µ )T... L a leave the lagrangian invariant L L When is local Lorentz symmetry spontaneously broken?
18 Local SLV occurs when a local tensor has a nonzero vev vacuum breaks Lorentz symmetry get fixed background tensors in local frames can introduce a tensor vev using a potential V has a minimum for a nonzero local vev where quadratic potential
19 In gauge theory SSB has well known consequences: (1) Goldstone Thm: when a global continuous sym is spontaneously broken massless Nambu-Goldstone (NG) modes appear (2) Higgs mechanism: if the symmetry is local the NG modes can give rise to massive gauge-boson modes. e.g. W,Z bosons acquire mass (3) Higgs modes: depending on the shape of the potential, additional massive modes can appear as well e.g. Higgs boson
20 With SSB the theory has multiple potential vacuum solutions V = 0 in the minimum A vacuum solution is Spontaneously chosen NG excitations stay inside the potential minimum obey V = 0 Massive Higgs modes climb up the potential walls obey V 0
21 Question: Can NG modes or a Higgs mechanism occur if Lorentz symmetry is spontaneously broken? If NG modes exist, they might possibly be: known particles (photons, gravitons) noninteracting or auxiliary modes gauged into gravitational sector (modified gravity) eaten (Higgs mechanism) Can use models with SLV to address these questions: Bumblebee models Cardinal models B µ A µ photons? C µ g µ gravitons? Antisymmetric two-tensor models
22 III. Nambu-Goldstone Modes & Higgs Mech. Consider a theory with a tensor vev in a local Lorentz frame: spontaneously breaks local Lorentz symmetry The vacuum vierbein is also a constant or fixed function e.g., assume a background Minkowski space with vierbein vev The spacetime tensor therefore also has a vev: spontaneously breaks diffeomorphisms Spontaneous breaking of local Lorentz symmetry implies spontaneous breaking of diffeomorphisms
23 How many NG (or would-be NG) modes can there be? Can have up to 6 broken Lorentz generators 4 broken diffeomorphisms There are potentially 10 NG modes when Lorentz symmetry is spontaneously broken Where are they? answer in general is gauge dependent But for one choice of gauge can put them all in the vierbein No Lorentz SSB has 16 components - 6 Lorentz degrees of freedom - 4 diff degrees of freedom up to 6 gravity modes (GR has only 2) With Lorentz SSB all 16 modes can potentially propagate
24 Perturbative analysis: Small fluctuations can drop distinction between local & spacetime indices Vacuum 10 symmetric comps. 6 antisymmetric comps. NG Modes: The NG modes are the excitations from the vacuum generated by the broken generators that maintain the extremum of the action: in general there are many such possible excitations
25 Lorentz & diffeo NG excitations maintain tensor magnitudes where Note: condition also follows from an SSB potential of form minimum of V <T> = t This condition is satisfied by: the vierbein contains the NG excitations
26 Expand the vierbein to identify the NG modes NG excitations: The combination contains the NG degrees of freedom Can find an effective theory for the NG modes by performing small virtual particle transformations from the vacuum and promoting the excitations to fields.
27 Under LLTs: (leading order) Under diffs: Promote the NG excitations to fields: write down an effective theory for them
28 Results: we find that the propagation & interactions of the NG modes depends on a number of factors: Geometry VEV Ghosts - Minkowski - Riemann - Riemann-Cartan - constant vs. nonconstant <T> - kinetic terms with ghost modes permit propagation of additional NG modes How many NG modes there are in a given theory will in general depend on all these quantities As an example, will consider a vector model in Riemann spacetime and in Riemann-Cartan spacetime.
29 Can a Higgs mechanisms occur? there are 2 types of NG modes (Lorentz & diffs) therefore have potentially 2 types of Higgs mechanisms diffeomorphism modes: can a Higgs mechanism occur for the diffs? does the vierbein (or metric) acquire a mass? conventional mass term connection depends on derivatives of the metric no mass term for the vierbein (or metric) itself No conventional Higgs mechanism for the metric (no mass term generated by covariant derivatives) but propagation of gravitational radiation is affected
30 Lorentz modes: go to local frame (using vierbein) gauge fields of Lorentz symmetry Get quadratic mass terms for the spin connection suggests a Higgs mechanism is possible for ω µ ab only works with dynamical torsion allowing propagation of ω µ ab Lorentz Higgs mechanism only in Riemann-Cartan spacetime offers new possibilities for model building theories with dynamical propagating spin connection finding models with no ghosts or tachyons is challenging
31 Are there additional massive Higgs modes? consider excitations away from the potential minimum unconventional mass term different from nonabelian gauge theory (no A µ in V) here the gauge field (metric) enters in V metric and tensor combine as additional massive modes Expand Find mass terms for combination of and appear as excitations with SLV can give rise to massive Higgs modes involving the metric
32 IV. Example: Bumblebee Models Gravity theories with a vector field and a potential term that induces spontaneous Lorentz breaking vector field Potential Vev Note: BB models do not have local U(1) gauge invariance (destroyed by presence of the potential V) Bumblebees: theoretically cannot fly (and yet they do) First restrict to Riemann spacetime (no torsion) no Higgs mechanism for Lorentz NG modes Will then look at possibility of a Higgs Mechanism
33 Bumblebee Lagrangian: L = 1 16 G (R 2 )+L B V (B µ B µ ± b 2 )+L int minimum of V gives the vev Have different choices for the kinetic, potential, & int terms depending on the interpretation of the vector For B µ L vector in a vector-tensor theory of gravity set L int =0 gravitational couplings only Or for B µ L generalized vector potential (photons?) keep L int =0 allows Lorentz violating matter ints
34 Bumblebee Kinetic Terms: (1) B µ as in a vector-tensor theory of gravity models with Will-Nordvedt kinetic terms L B =+ 1 B µ B R µ + 2 B µ B µ R 1 4 1B µ B µ D µ B D µ B D µ B µ D B expect propagating ghost modes (2) B µ as a generalized vector potential Kostelecky-Samuel models L B = 1 4 B µ B µ no propagating ghost modes charged matter interactions with global U(1) charge
35 Bumblebee Potential Terms: (1) Lagrange-multiplier potential freezes out massive mode appears as an extra field (2) Smooth quadratic potential allows massive-mode field no Lagrange multiplier Both exclude local U(1) symmetry
36 NG & massive modes: Examine different types of bumblebee models to look at the: degrees of freedom behavior of NG & massive modes Are the models stable (positive Hamiltonian)? e.g., flat spacetime with a timelike vev initial values with H H < 0 exist ultimately means bumblebee models are useful at low energy as effective or approx theories KS models can perform a Hamiltonian constraint analysis can find subspace of phase space with λ = 0 (Lagrange-multiplier V) large mass limit (quadratic V) H b µ =(b, 0, 0, 0) H > 0 in these subspaces, the KS model matches EM
37 Example: KS Bumblebee model in Riemann spacetime field strength quadratic potential matter current timelike vev Expect up to 4 massless NG modes what are they? do they propagate? No conventional Higgs mechanism Riemannn spacetime Theory can have a massive mode how does it affect gravity?
38 Equations of motion: where NG modes alone obey Einstein-Maxwell eqs massive mode obeys massive mode acts as source of charge & energy has nonlinear couplings to gravity and B µ equations can t be solved analytically
39 With global U(1) matter couplings can restrict to initial values that stabilize Hamiltonian conservation of conventional matter charge holds massive mode charge density decouples To illustrate the behavior of the NG & massive modes, it suffices to work with linearized equations of motion linearized theory is stable in flat-spacetime limit massive mode acts as source of charge & energy equations can be solved get that static massive mode the massive mode acts as a static primordial charge density that does not couple with matter current J µ
40 Fate of NG modes Find that the diff NG mode drops out of and the diff NG mode does not propagate it is purely an auxiliary field Find that the Lorentz NG modes propagate Lorentz NG excitations obey axial gauge condition removes massive mode from propagating degrees of freedom Lorentz NG modes are two transverse massless modes propagate as photons in axial gauge (linearized theory)
41 Idea of photons as NG modes Bjorken (1963) composite fermion models collective fermion excitations give rise to composite photons emerging as NG modes Nambu (1968) - local U(1) vector theory in nonlinear gauge has a nonzero vev for the EM field classically equivalent to electromagnetism Neither gives signals of physical Lorentz violation Here the KS bumblebee model is different has no local U(1) gauge invariance NG modes behave like photons has signatures of physical Lorentz violation includes gravity (local Lorentz symmetry)
42 Can the Einstein-Maxwell solutions originate out of a theory with spontaneous Lorentz violation but no local U(1) symmetry? To answer this, must look at effects of the massive mode models with massive modes are not equiv to EM Consider a point mass m with charge q in weak static limit usual potentials Introduce a potential for the massive mode modifies EM and gravitational fields modified Newtonian potential
43 Attempt to fit Special cases: (i) no charge couplings to yield a suitable form of that describes a modified theory of gravity models of dark matter? modified Newtonian potential (altered 1/r dependence) There are numerous examples that could be considered and decouple from matter purely modified gravity (no electromagnetism) NG modes not photons (what are they?) e.g., with Newton s constant rescales
44 (ii) no massive mode clearly the most natural choice and usual electromagnetic fields (iii) heavy massive mode usual Newtonian potential same solutions emerge with a massive mode when large mass limit The Einstein-Maxwell solution (with two massless transverse photons and the usual static potentials) emerges from the KS bumblebee with spontaneous Lorentz breaking but no local U(1) gauge symmetry matter interactions with b µ signal physical Lorentz breaking
45 Higgs Mechanism Riemann-Cartan Spacetime: and dynamical spin connection and (tetrad postulate) To quadratic order, the kinetic term becomes quadratic mass terms in ω µ ab Suggests a Higgs mechanism is possible for ω µ ab Note: Only works in the context of a theory with dynamical torsion allowing propagation of ω µ ab Can get a Higgs mechanism in Riemann-Cartan spacetime
46 Model Building in Riemann-Cartan Spacetime: consider propagating ω µ ab in a flat background need to add a kinetic term for ω µ ab Ghost-free models are extremely limited the massless modes must match with Results for ghost-free models: models with propagating massless ω µ ab exist e.g., but it is very hard to find a straightforward ghost-free Higgs mechanism for the spin connection it remains an open problem
47 Tensor Models Cardinal Model symmetric 2-tensor C µν in Minkowski space with SLV NG modes obey linearized Einstein eqs in fixed gauge nonlinear theory generated using a bootstrap mechanism alternate theory of gravity that contains GR at low energy Phon Model anti-symmetric 2-tensor B µν coupled to gravity with SLV up to 4 NG modes called phon modes (phonene) certain models produce a scalar (inflaton scenarios) massive modes exist that can modify gravity
48 V. Conclusions In gravity models with spontaneous Lorentz breaking diffeomorphisms also spontaneously broken both NG and massive modes can appear Gravitational Higgs effect depends on the geometry -Riemann-Cartan spacetime: possibility of a Higgs mech. for spin connection -Riemann spacetime: no conventional Higgs mech. for the metric but massive Higgs modes can involve the metric massive modes can affect the Newtonian potential Bumblebee Models NG modes propagate like massless photons massive mode modifies Newtonian potential Einstein-Maxwell solution is special case
49 Open Issues & Questions Physically viable models with SLV? è must eliminate ghosts è quantization è Higgs mechanism with massive spin connection è photon models with signatures of SLV SME with gravity è role of NG modes in gravitational sector? è massive Higgs modes? è origin of SME coefficients? Primary References: Kostelecky & Samuel, PRD 40 (1989) 1886 Kostelecky, PRD 69 (2004) RB & Kostelecky, PRD 71 (2005) RB, Fung & Kostelecky, PRD 77 (2008) RB, Gagne, Potting, & Vrublevskis, PRD 77 (2008)
50
Gravitational Tests 1: Theory to Experiment
Gravitational Tests 1: Theory to Experiment Jay D. Tasson St. Olaf College outline sources of basic information theory to experiment intro to GR Lagrangian expansion in gravity addressing the fluctuations
More informationNew Model of massive spin-2 particle
New Model of massive spin-2 particle Based on Phys.Rev. D90 (2014) 043006, Y.O, S. Akagi, S. Nojiri Phys.Rev. D90 (2014) 123013, S. Akagi, Y.O, S. Nojiri Yuichi Ohara QG lab. Nagoya univ. Introduction
More informationChris Verhaaren Joint Theory Seminar 31 October With Zackaria Chacko, Rashmish Mishra, and Simon Riquelme
Chris Verhaaren Joint Theory Seminar 31 October 2016 With Zackaria Chacko, Rashmish Mishra, and Simon Riquelme It s Halloween A time for exhibiting what some find frightening And seeing that it s not so
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 informationManifestly diffeomorphism invariant classical Exact Renormalization Group
Manifestly diffeomorphism invariant classical Exact Renormalization Group Anthony W. H. Preston University of Southampton Supervised by Prof. Tim R. Morris Talk prepared for Asymptotic Safety seminar,
More informationSymmetries, Groups Theory and Lie Algebras in Physics
Symmetries, Groups Theory and Lie Algebras in Physics M.M. Sheikh-Jabbari Symmetries have been the cornerstone of modern physics in the last century. Symmetries are used to classify solutions to physical
More informationStephen Blaha, Ph.D. M PubHsMtw
Quantum Big Bang Cosmology: Complex Space-time General Relativity, Quantum Coordinates,"Dodecahedral Universe, Inflation, and New Spin 0, 1 / 2,1 & 2 Tachyons & Imagyons Stephen Blaha, Ph.D. M PubHsMtw
More informationLecture III: Higgs Mechanism
ecture III: Higgs Mechanism Spontaneous Symmetry Breaking The Higgs Mechanism Mass Generation for eptons Quark Masses & Mixing III.1 Symmetry Breaking One example is the infinite ferromagnet the nearest
More informationPRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in
LONDON BEIJING HONG TSINGHUA Report and Review in Physics Vol2 PRINCIPLES OF PHYSICS From Quantum Field Theory to Classical Mechanics Ni Jun Tsinghua University, China NEW JERSEY \Hp SINGAPORE World Scientific
More informationFirst structure equation
First structure equation Spin connection Let us consider the differential of the vielbvein it is not a Lorentz vector. Introduce the spin connection connection one form The quantity transforms as a vector
More informationNote 1: Some Fundamental Mathematical Properties of the Tetrad.
Note 1: Some Fundamental Mathematical Properties of the Tetrad. As discussed by Carroll on page 88 of the 1997 notes to his book Spacetime and Geometry: an Introduction to General Relativity (Addison-Wesley,
More information2T-physics and the Standard Model of Particles and Forces Itzhak Bars (USC)
2T-physics and the Standard Model of Particles and Forces Itzhak Bars (USC) hep-th/0606045 Success of 2T-physics for particles on worldlines. Field theory version of 2T-physics. Standard Model in 4+2 dimensions.
More informationTowards a manifestly diffeomorphism invariant Exact Renormalization Group
Towards a manifestly diffeomorphism invariant Exact Renormalization Group Anthony W. H. Preston University of Southampton Supervised by Prof. Tim R. Morris Talk prepared for UK QFT-V, University of Nottingham,
More informationGravity, Lorentz violation, and the standard model
PHYSICAL REVIEW D 69, 105009 2004 Gravity, Lorentz violation, and the standard model V. Alan Kostelecký Physics Department, Indiana University, Bloomington, Indiana 47405, USA Received 8 January 2004;
More informationThe Standard Model of Electroweak Physics. Christopher T. Hill Head of Theoretical Physics Fermilab
The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab Lecture I: Incarnations of Symmetry Noether s Theorem is as important to us now as the Pythagorean Theorem
More informationChern-Simons Theory and Its Applications. The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee
Chern-Simons Theory and Its Applications The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee Maxwell Theory Maxwell Theory: Gauge Transformation and Invariance Gauss Law Charge Degrees of
More informationarxiv: v1 [hep-ph] 16 Aug 2012
Low Energy Tests of Lorentz and CPT Violation Don Colladay 5800 Bay Shore Road, New College of Florida arxiv:1208.3474v1 [hep-ph] 16 Aug 2012 Abstract. An overview of the theoretical framework of the Standard
More informationLecture 03. The Standard Model of Particle Physics. Part II The Higgs Boson Properties of the SM
Lecture 03 The Standard Model of Particle Physics Part II The Higgs Boson Properties of the SM The Standard Model So far we talked about all the particles except the Higgs If we know what the particles
More informationEn búsqueda del mundo cuántico de la gravedad
En búsqueda del mundo cuántico de la gravedad Escuela de Verano 2015 Gustavo Niz Grupo de Gravitación y Física Matemática Grupo de Gravitación y Física Matemática Hoy y Viernes Mayor información Quantum
More informationOn the uniqueness of Einstein-Hilbert kinetic term (in massive (multi-)gravity)
On the uniqueness of Einstein-Hilbert kinetic term (in massive (multi-)gravity) Andrew J. Tolley Case Western Reserve University Based on: de Rham, Matas, Tolley, ``New Kinetic Terms for Massive Gravity
More informationHiggs Field and Quantum Gravity
Higgs Field and Quantum Gravity The magnetic induction creates a negative electric field, causing an electromagnetic inertia responsible for the relativistic mass change; it is the mysterious Higgs Field
More informationLecture 7 SUSY breaking
Lecture 7 SUSY breaking Outline Spontaneous SUSY breaking in the WZ-model. The goldstino. Goldstino couplings. The goldstino theorem. Reading: Terning 5.1, 5.3-5.4. Spontaneous SUSY Breaking Reminder:
More informationInflationary Massive Gravity
New perspectives on cosmology APCTP, 15 Feb., 017 Inflationary Massive Gravity Misao Sasaki Yukawa Institute for Theoretical Physics, Kyoto University C. Lin & MS, PLB 75, 84 (016) [arxiv:1504.01373 ]
More informationQuantum Physics and General Relativity
Quantum Physics and General Relativity The self maintained electric potential of the accelerating charges equivalent with the General Relativity space-time curvature, and since it is true on the quantum
More informationarxiv:hep-ph/ v1 1 Feb 2005
Vector Goldstone Boson and Lorentz Invariance arxiv:hep-ph/050011v1 1 Feb 005 Ling-Fong Li Department of Physics, Carnegie Mellon University, Pittsburgh, PA 1513 January 5, 018 Abstract Spontanous symmetry
More informationEinstein-aether waves
Einstein-aether waves T. Jacobson* Insitut d Astrophysique de Paris, 98 bis Bvd. Arago, 75014 Paris, France D. Mattingly Department of Physics, University of California Davis, Davis, California 95616,
More information9 Quantum Field Theory for Children
101 9 Quantum Field Theory for Children The theories (known and hypothetical) needed to describe the (very) early universe are quantum field theories (QFT). The fundamental entities of these theories are
More informationChapter 2: Deriving AdS/CFT
Chapter 8.8/8.87 Holographic Duality Fall 04 Chapter : Deriving AdS/CFT MIT OpenCourseWare Lecture Notes Hong Liu, Fall 04 Lecture 0 In this chapter, we will focus on:. The spectrum of closed and open
More informationFrom Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics: measurements and uncertainty Smashing things together: from Rutherford to the LHC Particle Interactions Quarks
More informationQuentin Bailey Department of Physics and Astronomy Embry-Riddle Aeronautical University, Prescott, AZ
Quentin Bailey Department of Physics and Astronomy Embry-Riddle Aeronautical University, Prescott, AZ Third IUCSS Summer School and Workshop on the Lorentz- and CPT-violating Standard-Model Extension,
More informationchapter 3 Spontaneous Symmetry Breaking and
chapter 3 Spontaneous Symmetry Breaking and Nambu-Goldstone boson History 1961 Nambu: SSB of chiral symmetry and appearance of zero mass boson Goldstone s s theorem in general 1964 Higgs (+others): consider
More informationFinal Exam: Sat. Dec. 18, 2:45-4:45 pm, 1300 Sterling Exam is cumulative, covering all material. From last time
Final Exam: Sat. Dec. 18, 2:45-4:45 pm, 1300 Sterling Exam is cumulative, covering all material From last time Quantum field theory is a relativistic quantum theory of fields and interactions. Fermions
More informationSuper Yang-Mills Theory in 10+2 dims. Another Step Toward M-theory
1 Super Yang-Mills Theory in 10+2 dims. Another Step Toward M-theory Itzhak Bars University of Southern California Talk at 4 th Sakharov Conference, May 2009 http://physics.usc.edu/~bars/homepage/moscow2009_bars.pdf
More informationMaxwell s equations. electric field charge density. current density
Maxwell s equations based on S-54 Our next task is to find a quantum field theory description of spin-1 particles, e.g. photons. Classical electrodynamics is governed by Maxwell s equations: electric field
More informationGravitational Waves. GR: 2 polarizations
Gravitational Waves GR: 2 polarizations Gravitational Waves GR: 2 polarizations In principle GW could have 4 other polarizations 2 vectors 2 scalars Potential 4 `new polarizations Massive Gravity When
More informationAnalyzing WMAP Observation by Quantum Gravity
COSMO 07 Conference 21-25 August, 2007 Analyzing WMAP Observation by Quantum Gravity Ken-ji Hamada (KEK) with Shinichi Horata, Naoshi Sugiyama, and Tetsuyuki Yukawa arxiv:0705.3490[astro-ph], Phys. Rev.
More informationPart III. Interacting Field Theory. Quantum Electrodynamics (QED)
November-02-12 8:36 PM Part III Interacting Field Theory Quantum Electrodynamics (QED) M. Gericke Physics 7560, Relativistic QM 183 III.A Introduction December-08-12 9:10 PM At this point, we have the
More informationNew Fundamental Wave Equation on Curved Space-Time and its Cosmological Applications
New Fundamental Wave Equation on Curved Space-Time and its Cosmological Applications Z.E. Musielak, J.L. Fry and T. Chang Department of Physics University of Texas at Arlington Flat Space-Time with Minkowski
More informationHIGHER SPIN PROBLEM IN FIELD THEORY
HIGHER SPIN PROBLEM IN FIELD THEORY I.L. Buchbinder Tomsk I.L. Buchbinder (Tomsk) HIGHER SPIN PROBLEM IN FIELD THEORY Wroclaw, April, 2011 1 / 27 Aims Brief non-expert non-technical review of some old
More informationAs usual, these notes are intended for use by class participants only, and are not for circulation. Week 8: Lectures 15, 16
As usual, these notes are intended for use by class participants only, and are not for circulation. Week 8: Lectures 15, 16 Masses for Vectors: the Higgs mechanism April 6, 2012 The momentum-space propagator
More informationA brief introduction to modified theories of gravity
(Vinc)Enzo Vitagliano CENTRA, Lisboa May, 14th 2015 IV Amazonian Workshop on Black Holes and Analogue Models of Gravity Belém do Pará The General Theory of Relativity dynamics of the Universe behavior
More informationGraviton contributions to the graviton self-energy at one loop order during inflation
Graviton contributions to the graviton self-energy at one loop order during inflation PEDRO J. MORA DEPARTMENT OF PHYSICS UNIVERSITY OF FLORIDA PASI2012 1. Description of my thesis problem. i. Graviton
More informationCoupled Dark Energy and Dark Matter from dilatation symmetry
Coupled Dark Energy and Dark Matter from dilatation symmetry Cosmological Constant - Einstein - Constant λ compatible with all symmetries Constant λ compatible with all observations No time variation in
More informationOrigin of the Photon Mass and ECE Spin Field in the Spin Connection of Space-Time
12 Origin of the Photon Mass and ECE Spin Field in the Spin Connection of Space-Time by Myron W. Evans, Alpha Institute for Advanced Study, Civil List Scientist. (emyrone@aol.com and www.aias.us) Abstract
More informationGravity and action at a distance
Gravitational waves Gravity and action at a distance Newtonian gravity: instantaneous action at a distance Maxwell's theory of electromagnetism: E and B fields at distance D from charge/current distribution:
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 informationThe 2015 Data Tables for Lorentz and CPT Violation
The 2015 Data Tables for Lorentz and CPT Violation Reviews of Modern Physics 83, 11 (2011) update: arxiv:0801.0287v8 (January 2015) Kostelecký, NR Second IUCSS Summer School on the Lorentz- and CPT-violating
More informationTests at Colliders. Summer School on the SME June 17, 2018 Mike Berger. I. Top quark production and decay II. Neutral meson oscillations
Tests at Colliders Summer School on the SME June 17, 2018 Mike Berger I. Top quark production and decay II. Neutral meson oscillations Collider Physics 1. In principle, one has access (statistically) to
More informationThe mass of the Higgs boson
The mass of the Higgs boson LHC : Higgs particle observation CMS 2011/12 ATLAS 2011/12 a prediction Higgs boson found standard model Higgs boson T.Plehn, M.Rauch Spontaneous symmetry breaking confirmed
More informationMetric-affine theories of gravity
Introduction Einstein-Cartan Poincaré gauge theories General action Higher orders EoM Physical manifestation Summary and the gravity-matter coupling (Vinc) CENTRA, Lisboa 100 yy, 24 dd and some hours later...
More informationWeek 3: Renormalizable lagrangians and the Standard model lagrangian 1 Reading material from the books
Week 3: Renormalizable lagrangians and the Standard model lagrangian 1 Reading material from the books Burgess-Moore, Chapter Weiberg, Chapter 5 Donoghue, Golowich, Holstein Chapter 1, 1 Free field Lagrangians
More informationScale symmetry a link from quantum gravity to cosmology
Scale symmetry a link from quantum gravity to cosmology scale symmetry fluctuations induce running couplings violation of scale symmetry well known in QCD or standard model Fixed Points Quantum scale symmetry
More informationOne-loop renormalization in a toy model of Hořava-Lifshitz gravity
1/0 Università di Roma TRE, Max-Planck-Institut für Gravitationsphysik One-loop renormalization in a toy model of Hořava-Lifshitz gravity Based on (hep-th:1311.653) with Dario Benedetti Filippo Guarnieri
More informationScale-invariant alternatives to general relativity
Scale-invariant alternatives to general relativity Mikhail Shaposhnikov Zurich, 21 June 2011 Zurich, 21 June 2011 p. 1 Based on: M.S., Daniel Zenhäusern, Phys. Lett. B 671 (2009) 162 M.S., Daniel Zenhäusern,
More informationSearches for Local Lorentz Violation
Searches for Local Lorentz Violation Jay D. Tasson St. Olaf College outline background motivation SME gravity theory pure-gravity sector matter-gravity couplings experiments & observations motivation E
More information11 Group Theory and Standard Model
Physics 129b Lecture 18 Caltech, 03/06/18 11 Group Theory and Standard Model 11.2 Gauge Symmetry Electromagnetic field Before we present the standard model, we need to explain what a gauge symmetry is.
More informationHunting New Physics in the Higgs Sector
HS Hunting New Physics in the Higgs Sector SM Higgs Sector - Test of the Higgs Mechanism Oleg Kaikov KIT, Seminar WS 2015/16 Prof. Dr. M. Margarete Mühlleitner, Dr. Roger Wolf, Dr. Hendrik Mantler Advisor:
More informationConservation Theorem of Einstein Cartan Evans Field Theory
28 Conservation Theorem of Einstein Cartan Evans Field Theory by Myron W. Evans, Alpha Institute for Advanced Study, Civil List Scientist. (emyrone@aol.com and www.aias.us) Abstract The conservation theorems
More informationUNIVERSITY OF CRAIOVA FACULTY OF PHYSICS DAN CORNEA. Summary of Ph.D. THESIS
UNIVERSITY OF CRAIOVA FACULTY OF PHYSICS DAN CORNEA Summary of Ph.D. THESIS COHOMOLOGICAL APPROACHES TO EINSTEIN-HILBERT GRAVITY Ph.D. supervisor Prof. dr. CONSTANTIN BIZDADEA CRAIOVA 2008 Contents 1 Introduction
More informationTwo Fundamental Principles of Nature s Interactions
Two Fundamental Principles of Nature s Interactions Tian Ma, Shouhong Wang Supported in part by NSF, ONR and Chinese NSF http://www.indiana.edu/ fluid I. Gravity and Principle of Interaction Dynamics PID)
More informationMaxwell s equations. based on S-54. electric field charge density. current density
Maxwell s equations based on S-54 Our next task is to find a quantum field theory description of spin-1 particles, e.g. photons. Classical electrodynamics is governed by Maxwell s equations: electric field
More informationHolographic self-tuning of the cosmological constant
Holographic self-tuning of the cosmological constant Francesco Nitti Laboratoire APC, U. Paris Diderot IX Crete Regional Meeting in String Theory Kolymbari, 10-07-2017 work with Elias Kiritsis and Christos
More informationDark Energy Screening Mechanisms. Clare Burrage University of Nottingham
Dark Energy Screening Mechanisms Clare Burrage University of Nottingham The expansion of the Universe is accelerating "for the discovery of the accelerating expansion of the Universe through observations
More informationA Brief Introduction to AdS/CFT Correspondence
Department of Physics Universidad de los Andes Bogota, Colombia 2011 Outline of the Talk Outline of the Talk Introduction Outline of the Talk Introduction Motivation Outline of the Talk Introduction Motivation
More informationNew Geometric Formalism for Gravity Equation in Empty Space
New Geometric Formalism for Gravity Equation in Empty Space Xin-Bing Huang Department of Physics, Peking University, arxiv:hep-th/0402139v3 10 Mar 2004 100871 Beijing, China Abstract In this paper, complex
More informationarxiv:hep-th/ v1 10 Dec 2003
HUTP-03/A081 UMD-PP-04-012 Ghost Condensation and a Consistent Infrared Modification of Gravity arxiv:hep-th/0312099v1 10 Dec 2003 Nima Arkani-Hamed a, Hsin-Chia Cheng a, Markus A. Luty a,b,c, Shinji Mukohyama
More informationElectroweak and Higgs Physics
Electroweak and Higgs Physics Lecture 2 : Higgs Mechanism in the Standard and Supersymmetric Models Alexei Raspereza DESY Summer Student Program Hamburg August 2017 Standard Model (Summary) Building blocks
More informationThe Dark Side of the Higgs Field and General Relativity
The Dark Side of the Higgs Field and General Relativity The gravitational force attracting the matter, causing concentration of the matter in a small space and leaving much space with low matter concentration:
More informationEmergent gravity. Diana Vaman. Physics Dept, U. Virginia. September 24, U Virginia, Charlottesville, VA
Emergent gravity Diana Vaman Physics Dept, U. Virginia September 24, U Virginia, Charlottesville, VA What is gravity? Newton, 1686: Universal gravitational attraction law F = G M 1 M 2 R 2 12 Einstein,
More informationWhy we need quantum gravity and why we don t have it
Why we need quantum gravity and why we don t have it Steve Carlip UC Davis Quantum Gravity: Physics and Philosophy IHES, Bures-sur-Yvette October 2017 The first appearance of quantum gravity Einstein 1916:
More informationelectrodynamics and Lorentz violation
Vacuum Cherenkov radiation in Lorentz violating quantum electrodynamics and experimental limits on the scale of Lorentz violation Damiano Anselmi (IHEP/CAS, Beijing, & Pisa University) Lorentz symmetry
More informationThe Standard Model Part. II
Our Story Thus Far The Standard Model Part. II!!We started with QED (and!)!!we extended this to the Fermi theory of weak interactions! Adding G F!!Today we will extended this to Glashow-Weinberg-Salam
More informationNonsingular big-bounce cosmology from spin and torsion
Nonsingular big-bounce cosmology from spin and torsion Nikodem J. Popławski Department of Physics, Indiana University, Bloomington, IN 22 nd Midwest Relativity Meeting University of Chicago, Chicago, IL
More informationSpecial Relativity from Soft Gravitons
Special Relativity from Soft Gravitons Mark Hertzberg, Tufts University CosPA, December 14, 2017 with McCullen Sandora, PRD 96 084048 (1704.05071) Can the laws of special relativity be violated in principle?
More informationElementary particles and typical scales in high energy physics
Elementary particles and typical scales in high energy physics George Jorjadze Free University of Tbilisi Zielona Gora - 23.01.2017 GJ Elementary particles and typical scales in HEP Lecture 1 1/18 Contents
More informationGravitational Čerenkov Notes
Gravitational Čerenkov Notes These notes were presented at the IUCSS Summer School on the Lorentz- and CPT-violating Standard-Model Extension. They are based Ref. [1]. There are no new results here, and
More informationQuantum Field Theory Notes. Ryan D. Reece
Quantum Field Theory Notes Ryan D. Reece November 27, 2007 Chapter 1 Preliminaries 1.1 Overview of Special Relativity 1.1.1 Lorentz Boosts Searches in the later part 19th century for the coordinate transformation
More informationNew Geometric Formalism for Gravity Equation in Empty Space
New Geometric Formalism for Gravity Equation in Empty Space Xin-Bing Huang Department of Physics, Peking University, arxiv:hep-th/0402139v2 23 Feb 2004 100871 Beijing, China Abstract In this paper, complex
More informationHIGGS-GRAVITATIONAL INTERATIONS! IN PARTICLE PHYSICS & COSMOLOGY
HIGGS-GRAVITATIONAL INTERATIONS! IN PARTICLE PHYSICS & COSMOLOGY beyond standard model ZHONG-ZHI XIANYU Tsinghua University June 9, 015 Why Higgs? Why gravity? An argument from equivalence principle Higgs:
More informationFundamental Theories of Physics in Flat and Curved Space-Time
Fundamental Theories of Physics in Flat and Curved Space-Time Zdzislaw Musielak and John Fry Department of Physics The University of Texas at Arlington OUTLINE General Relativity Our Main Goals Basic Principles
More informationQuantum Field Theory. and the Standard Model. !H Cambridge UNIVERSITY PRESS MATTHEW D. SCHWARTZ. Harvard University
Quantum Field Theory and the Standard Model MATTHEW D. Harvard University SCHWARTZ!H Cambridge UNIVERSITY PRESS t Contents v Preface page xv Part I Field theory 1 1 Microscopic theory of radiation 3 1.1
More informationLecture 6 The Super-Higgs Mechanism
Lecture 6 The Super-Higgs Mechanism Introduction: moduli space. Outline Explicit computation of moduli space for SUSY QCD with F < N and F N. The Higgs mechanism. The super-higgs mechanism. Reading: Terning
More informationDirac Equation with Self Interaction Induced by Torsion
Advanced Studies in Theoretical Physics Vol. 9, 2015, no. 12, 587-594 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/astp.2015.5773 Dirac Equation with Self Interaction Induced by Torsion Antonio
More informationQuantum Gravity and Entanglement
Quantum Gravity and Entanglement The magnetic induction creates a negative electric field, causing an electromagnetic inertia responsible for the relativistic mass change; it is the mysterious Higgs Field
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 informationGeneration of Large-Scale Magnetic Fields from Inflation in Teleparallelism
VIIIth Rencontres du Vietnam - Beyond the Standard Model Generation of Large-Scale Magnetic Fields from Inflation in Teleparallelism Reference: JCAP 10 (2012) 058 Ling-Wei Luo Department of Physics, National
More informationGravitational wave memory and gauge invariance. David Garfinkle Solvay workshop, Brussels May 18, 2018
Gravitational wave memory and gauge invariance David Garfinkle Solvay workshop, Brussels May 18, 2018 Talk outline Gravitational wave memory Gauge invariance in perturbation theory Perturbative and gauge
More informationStability and Instability of Black Holes
Stability and Instability of Black Holes Stefanos Aretakis September 24, 2013 General relativity is a successful theory of gravitation. Objects of study: (4-dimensional) Lorentzian manifolds (M, g) which
More information1 Canonical quantization conformal gauge
Contents 1 Canonical quantization conformal gauge 1.1 Free field space of states............................... 1. Constraints..................................... 3 1..1 VIRASORO ALGEBRA...........................
More informationIntroduction to the Vainshtein mechanism
Introduction to the Vainshtein mechanism Eugeny Babichev LPT, Orsay School Paros 23-28 September 2013 based on arxiv:1107.1569 with C.Deffayet OUTLINE Introduction and motivation k-mouflage Galileons Non-linear
More informationHolographic self-tuning of the cosmological constant
Holographic self-tuning of the cosmological constant Francesco Nitti Laboratoire APC, U. Paris Diderot IX Aegean Summer School Sifnos, 19-09-2017 work with Elias Kiritsis and Christos Charmousis, 1704.05075
More informationScale invariance and the electroweak symmetry breaking
Scale invariance and the electroweak symmetry breaking Archil Kobakhidze School of Physics, University of Melbourne R. Foot, A.K., R.R. Volkas, Phys. Lett. B 655,156-161,2007 R. Foot, A.K., K.L. Mcdonald,
More informationEinstein Double Field Equations
Einstein Double Field Equations Stephen Angus Ewha Woman s University based on arxiv:1804.00964 in collaboration with Kyoungho Cho and Jeong-Hyuck Park (Sogang Univ.) KIAS Workshop on Fields, Strings and
More informationThe cosmological constant puzzle
The cosmological constant puzzle Steven Bass Cosmological constant puzzle: Accelerating Universe: believed to be driven by energy of nothing (vacuum) Vacuum energy density (cosmological constant or dark
More informationCosmology and Gravitational Bags via Metric-Independent Volume-Form Dynamics
1 Cosmology and Gravitational Bags via Metric-Independent Volume-Form Dynamics XI International Workshop Lie Theory and Its Applications, Varna 2015 Eduardo Guendelman 1, Emil Nissimov 2, Svetlana Pacheva
More informationBeyond the standard model? From last time. What does the SM say? Grand Unified Theories. Unifications: now and the future
From last time Quantum field theory is a relativistic quantum theory of fields and interactions. Fermions make up matter, and bosons mediate the forces by particle exchange. Lots of particles, lots of
More informationHiggs boson may appear to be a technihiggs
Higgs boson may appear to be a technihiggs The discovered elusive Higgs boson, first predicted theoretically, turns out to may have been a different particle after all. A team of international researchers
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 informationGravitational Magnetic Force
Gravitational Magnetic Force The curved space-time around current loops and solenoids carrying arbitrarily large steady electric currents is obtained from the numerical resolution of the coupled Einstein-Maxwell
More informationGravity, Strings and Branes
Gravity, Strings and Branes Joaquim Gomis International Francqui Chair Inaugural Lecture Leuven, 11 February 2005 Fundamental Forces Strong Weak Electromagnetism QCD Electroweak SM Gravity Standard Model
More information