Continuum limit of fishnet graphs and AdS sigma model
|
|
- Karin Felicity Bates
- 5 years ago
- Views:
Transcription
1 Continuum limit of fishnet graphs and AdS sigma model Benjamin Basso LPTENS 15th Workshop on Non-Perturbative QCD, IAP, Paris, June 2018 based on work done in collaboration with De-liang Zhong
2 Motivation Understand dynamics of planar graphs and its relation to sigma models [ t Hooft] Best possible starting point: N=4 SYM [Maldacena 97] String dual is believed to be known Theory is believed to be integrable (meaning we have methods for re-summing planar graphs) Use solution to gain knowledge about other models by deforming / twisting the theory Partial re-summation of planar graphs (Reduce complexity, but maintain as many important properties as possible: conformal symmetry, integrability, etc.)
3 Fishnet theory Baby version of N = 4 SYM A theory for matrix scalar fields with quartic coupling L fishnet = Ntr apple [Gurdogan,Kazakov 15] [Caetano,Gurdogan,Kazakov µ µ 1 µ µ 2 +(4 g) It can be obtained by twisting N=4 SYM theory, so-called sending the deformation parameter to i-infinity while taking YM coupling to zero deformation, [Frolov 05] [Lunin,Maldacena 05] [Grabner,Gromov,Kazakov,Korchemsky 17] [Sieg,Wilhelm 16] 1. Gluons and gauginos decouple 2. Gauge group becomes a flavour group 3. Conformal symmetry is preserved for any coupling (at least in planar limit and for fine-tuned double-trace couplings) 4. Integrability is retained
4 Fishnet theory Baby version of N = 4 SYM A theory for matrix scalar fields with quartic coupling L fishnet = Ntr apple [Gurdogan,Kazakov 15] [Caetano,Gurdogan,Kazakov µ µ 1 µ µ 2 +(4 g) All planar graphs locally look the same Integrability is not mysterious here and links directly to basic property of the coupling in d=4 Win: simplicity, many fewer graphs Lose: unitarity 4 bulk graph [Zamolodchikov 80] [Isaev 03] [Gromov,Kazakov,Korchemsky,Negro,Sizov 17] [Chicherin,Kazakov,Loebbert,Muller,Zhong 16]
5 Continuum limit & string? What about duality to string in AdS? Extremal twisting procedure forces the YM coupling to be small String in highly curved AdS? Question: what is the continuum limit of the fishnet graphs? Important observation concerning large order behaviour [Zamolodchikov 80] Zamolodchikov s thermodynamical scaling log Z L,T = L T log g 2 cr g cr = (3/4) p (5/4) = Determine a critical coupling where graphs become dense
6 Plan Study continuum limit using integrable methods borrowed from N=4 SYM Probe: scaling dimension of BMN vacuum operator O =tr L 1 Qualitative picture of as function of coupling when L!1 g 2 L 2 1/4 g 2 cr g 2 Main claim : continuum limit is given by the 2d AdS5 sigma model BMN operator maps to tachyon tr L 1 $ V e i t Relation to sigma model energy log g 2L = log g 2L cr + E 2d (,L)
7 Graphs versus integrability Computation of anomalous dimension BMN vacuum tr L 1 (not protected) = L + [Gurdogan,Kazakov 15] [Caetano,Gurdogan,Kazakov 16] Graphs: loop corrections come from the wheel diagrams Z = wave-function renormalization 1 wheel 2 wheels g 2L g 4L Depends on cut off R log cut off Anomalous dimension controls the logarithmic dependence on cut off log Z R
8 Graphs versus integrability Computation of anomalous dimension BMN vacuum tr L 1 (not protected) = L + [Gurdogan,Kazakov 15] [Caetano,Gurdogan,Kazakov 16] Integrability: Free energy of a gas of magnons at temperature 1/L Partition function on R S L R Z L,R = X T >0 g 2LT L Each magnon carries a rapidity u, which is a momentum along euclidean time direction, and a discrete label a, which enumerates harmonics on 3-sphere log Z L,R = LR +... Weak coupling expansion: magnon = wheel u 1... u T Integrability: direct quantum mechanical interpretation of the graphs
9 Thermodynamical Bethe Ansatz Factorized scattering allows us to obtain free energy from TBA eqs = L 2 X Z du 2 Y a(u) a>1 X Z du 2 Y2 a(u) 2 X Z dudv (2 ) 2 Y a(u)k a,b (u, v)y b (v)+o(y 3 ) a>1 a,b>1 Boltzmann weight: Y a (u) =a 2 e Lh L a(u) 1 Mechanical energy: a (u) = log (u 2 + a 2 /4) Scattering kernel: K a,b (u, v) i@u log S a,b(u, v) + matrix part Coupling constant is just a fugacity for the magnons (wheels) g 2 = e h with h the chemical potential
10 Thermodynamical limit Thermodynamical limit L!1 Interesting when chemical potential gets bigger than mass of lightest magnon that is for h>log (u = 0) = log 1/4 g>1/2 h A Fermi sea forms All states below the Fermi rapidity are filled Increasing coupling amounts to increasing B occupied states Comment: only the s-wave (lightest) magnons condense (higher Lorentz harmonics decouple) Fermi rapidity
11 Linear integral equation In the thermodynamical regime the TBA eqs linearize Integral equation for the rapidity distribution of energy levels (u) =C BC: (u = ±B) =0 (u)+ Z B Effective chemical potential: C = log g 2 B du 2 K(u v) (v) Kernel: K(u) =2 (1 + iu)+2 (1 iu)+ 2 1+u 2 Z B B du 2 k(u) (u) Scaling dimension: /L =1 Z B B du (u)
12 Critical regime Small B : dilute gas, density of magnons is small j = df/dh 0 " = f + hj 1 Critical regime relates to large magnon density B!1 " j log g 2 cr f 0 All energy levels are filled Equation is solved in Fourier space cr(u) =C cr One verifies: (u)+ Z 1 1 (i) Scaling dimension vanishes dv 2 K(u v) cr(v) ) /L =0 cr = log with (ii) Chemical potential (coupling) approaches predicted value p 2 cosh +1 p 2 cosh 1 = u/2 cr e ) C cr =0 ) g cr = (3/4)/ p (5/4)
13 Numerical check Integral equation can be solved numerically 1.0 DêL g g thr =0.5 g cr = thermodynamical window
14 Near-critical regime Particle-hole transformation: Fermi sea of magnons dual Fermi sea Equation for dual excitations: Dualize kernel by means of K = K 1 K = K K K... Act on both sides of the equation with 1 K
15 Dual equation: No chemical potential but extra BC: Dual equations Dual energy formula: log g 2 = log g 2 cr + 1) Dual kernel: K( ) = ( ) =E( i@ log 2) Dual dispersion relation: Z 2 >B 2 d 0 2 K( 0 ) ( 0 ) Z 2 >B 2 i (1 + 2 ) ( 1 2 d 2 P 0 ( ) ( ) ( ) 2 log = /L = charge density E( ) = i 2 ) ( i (1 i 2 ) ( i 2 ) ( 3 4 cr ( ) = log i 2 ) 2 ) ( 1 4 i 2 ) ( i 2 ) applep 2 cosh +1 p 2 cosh 1 m 2 e P ( ) = ie( + i 2 )=i log applep 2 sinh + i p 2 sinh i m 2 e where m =4 p 2
16 Interpretation What is the dual system describing? 1) Kernel: K = i@ log S O(6) Excitations scatter as particles in 2d O(6) non-linear sigma model [Zamolodchikov&Zamolodchikov] 2) Dispersion relation: Energy sinh 2 ( 1 2 E)=sin2 ( 1 2 P ) 1.5 Gapless excitations (unlike O(6) model) Besides, E decreases when increases Support is non-compact and density is not normalizable (cannot count excitations) No mass gap + continuous spectrum Suggest: sigma model with non-compact target space Proposal: integrable lattice completion of sigma model AdS 5 Momentum
17 2d non-linear sigma model Sigma model with curved target space Weak coupling (large AdS radius) Beta function related to Ricci scalar 1 L = 2e 2 a X a X B e 2 1 For : AdS d+1 One loop running: Alternatively: Y Y 2? Y 2 d+1 = e2 (µ) = d 2 e4 (µ) e 2 (µ) = d 2 log ( /µ) 1. Theory is weakly coupled in IR 2. There is no mass gap 3. There is no isolated vacuum
18 Perturbative tachyon Consider sigma model on cylinder of radius L Interested in 2d ground state energy : tachyon (best candidate for extremum of energy at given charge = global time energy) V e i t Classically, it corresponds to solution Y 0 ± iy d+1 = e ±ih Y? =0 Charge density /L = 1 e 2 (Y 0 Ẏ d+1 Y d+1 Ẏ 0 )= H/e 2 Energy density E/L = 1 2e 2 (Ẏ 0 Ẏ 0 + Ẏ d+1 Ẏ d+1 )= H 2 /(2e 2 ) Classical result : (c-o-m energy) E = e2 2 Same as in O(d+2) model if not for the sign of the coupling e 2 $ e 2 2L
19 Back to numerics Quadratic Casimir scaling near critical point fits numerics DêL log g 2 /g 2 cr = e2 2 2L g g thr =0.5 g cr = thermodynamical window
20 Back to equation Compact case ( ) =m cosh + Z B B d 0 2 K O(6)( 0 ) ( 0 ) Eq. describes gas of massive excitations at finite particle density Systematic expansion is known in the large density regime B 1 [Volin 09] Non-compact case ( ) = m 2 e + Z ( 0 ) 2 >B 2 d 0 2 K O(6)( 0 ) ( 0 ) Eq. describes gas of massless excitations at finite charge density Despite being different, two problems are identical, to any order in if we flip the sign of Fermi rapidity B! B 1/B
21 All-order result Fermi parameter B 1/e 2 log (L/ ) 1 e 2 = coupling of sigma model at energy scale = /L Flipping the sign of the coupling e 2 $ e 2 Same as changing the sign of curvature non-compact L $ compact L Same as changing direction of RG flow Owing to this connection to the compact sigma model, the dual integral equation describes the tachyon of the AdS model to all orders in perturbation theory
22 TBA equations Original magnon TBA (massive + chemical potential) log Y 1 = L log g 2 L + K log (1 + Y 1 )+... coupling = input output : = L 1X a=1 (all blacks nodes contribute to energy) Z du log (1 + Y a) massive TBA Dual TBA (massless + no chemical potential) log Y 1 = LE K O(6) log (1 + 1/Y 1 )+... = input (tachyon rep) massless TBA (only 1 momentum carrier) coupling = output (sigma model energy) log g 2L /g 2L cr = Z d 2 P 0 ( ) log (1 + 1/Y 1 )
23 Central charge Analysis in CFT limit ( 1/L effect aka Casimir energy) Split into left and right movers = scale-invariant (kink) solution [Zamolodchikov 90s] [Klassen-Melzer 90s] Kink is characterized by its asymptotic values on far left and far right Standard analysis gives TBA central charge c = c 0 c 1 where c? = X i L( Y? i 1+Y? i with Rogers dilogarithm L(x) = 6 2 (Li 2(x)+ 1 2 ) log x log (1 x)) Stationary solutions to Y-system are known c 0 =7 c 1 =2 symmetric phase O(6) broken phase O(4) Central charge is as it should be c =5
24 CFT analysis Central charge agrees with perturbative analysis in the AdS sigma model = count of the number of Goldstone bosons Close to IR fixed point, i.e. large L, the 2d CFT gives information about the behaviour of the energy level Operator-state correspondence: energy maps to 2d anomalous dimension of vertex operator V e i t E 2d = c eff (L) 6L e 2 ( d) 2L + O(e 4 ) Effective central charge at distance L: c eff (L) =5+O(e 2 ) Running coupling at distance L: e 2 2 d log L
25 Conclusion Conjecture : 4d planar fishnet graphs define an integrable lattice regularization of the 2d AdS5 sigma model When all characteristic fishnet length scales are large, the sigma model description is weakly coupled This is applicable at large L and small quantum numbers
26 Outlook String worldsheet or not? We found a marginality condition of sort 0=Lµ + E 2d (L) with cosmological constant µ = log g 2 cr/g 2 Non-critical strings with a tunable intercept exist in flat space, at least classically Could it be that we are dealing with an AdS version of it? What seems to be clear is that the on-shell condition comes from the sum over the wheels X (g/g cr ) 2LT e TE 2d(L, ) = T >0 1 1 (g/g cr ) 2L e E 2d(L, ) with T acting as a discrete proper time (Schwinger parameter)
27 THANK YOU!
Seminar in Wigner Research Centre for Physics. Minkyoo Kim (Sogang & Ewha University) 10th, May, 2013
Seminar in Wigner Research Centre for Physics Minkyoo Kim (Sogang & Ewha University) 10th, May, 2013 Introduction - Old aspects of String theory - AdS/CFT and its Integrability String non-linear sigma
More informationHexagons and 3pt functions
Hexagons and 3pt functions Benjamin Basso ENS Paris Current Themes in Holography NBI Copenhagen 2016 based on work with Vasco Goncalves, Shota Komatsu and Pedro Vieira The spectral problem is solved O(x)
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 informationTowards solution of string theory in AdS3 x S 3
Towards solution of string theory in AdS3 x S 3 Arkady Tseytlin based on work with Ben Hoare: arxiv:1303.1037, 1304.4099 Introduction / Review S-matrix for string in AdS3 x S3 x T4 with RR and NSNS flux
More informationNumerics and strong coupling results in the planar AdS/CFT correspondence. Based on: Á. Hegedűs, J. Konczer: arxiv:
Numerics and strong coupling results in the planar AdS/CFT correspondence Based on: Á. Hegedűs, J. Konczer: arxiv:1604.02346 Outline Introduction : planar AdS/CFT spectral problem From integrability to
More informationSix-point gluon scattering amplitudes from -symmetric integrable model
YITP Workshop 2010 Six-point gluon scattering amplitudes from -symmetric integrable model Yasuyuki Hatsuda (YITP) Based on arxiv:1005.4487 [hep-th] in collaboration with K. Ito (TITECH), K. Sakai (Keio
More informationExact anomalous dimensions of 4-dimensional N=4 super-yang-mills theory in 'thooft limit
PACIFIC 2015 UCLA Symposium on Particle Astrophysics and Cosmology Including Fundamental Interactions September 12-19, 2015, Moorea, French Polynesia Exact anomalous dimensions of 4-dimensional N=4 super-yang-mills
More informationT-reflection and the vacuum energy in confining large N theories
T-reflection and the vacuum energy in confining large N theories Aleksey Cherman! FTPI, University of Minnesota! with Gokce Basar (Stony Brook -> U. Maryland),! David McGady (Princeton U.),! and Masahito
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 informationAnomalous Strong Coupling
Simons Center for Geometry and Physics, Stony Brook based on [Brenno Carlini Vallilo, LM, arxiv:1102.1219 [hep-th] ] for a pedagogical review, [LM, arxiv:1104.2604][hep-th] ] XI Workshop on Nonperturbative
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 informationEmergent geometry: seeing further from the shoulders of giants.
Emergent geometry: seeing further from the shoulders of giants. David Berenstein, UCSB. Chapel Hill, May 8, 2014 Based mostly on arxiv:1301.3519 + arxiv:1305.2394 w. E. Dzienkowski + work in progress.
More information1/N Expansions in String and Gauge Field Theories. Adi Armoni Swansea University
1/N Expansions in String and Gauge Field Theories Adi Armoni Swansea University Oberwoelz, September 2010 1 Motivation It is extremely difficult to carry out reliable calculations in the strongly coupled
More informationIntegrability of Conformal Fishnet Theory
Integrability of Conformal Fishnet Theory Gregory Korchemsky IPhT, Saclay In collaboration with David Grabner, Nikolay Gromov, Vladimir Kazakov arxiv:1711.04786 15th Workshop on Non-Perturbative QCD, June
More informationOne Loop Tests of Higher Spin AdS/CFT
One Loop Tests of Higher Spin AdS/CFT Simone Giombi UNC-Chapel Hill, Jan. 30 2014 Based on 1308.2337 with I. Klebanov and 1401.0825 with I. Klebanov and B. Safdi Massless higher spins Consistent interactions
More informationMagnon kinematics in planar N = 4 Yang-Mills
Magnon kinematics in planar N = 4 Yang-Mills Rafael Hernández, IFT-Madrid Collaboration with N. Beisert, C. Gómez and E. López Outline Introduction Integrability in the AdS/CFT correspondence The quantum
More informationIntegrability of spectrum of N=4 SYM theory
Todai/Riken joint workshop on Super Yang-Mills, solvable systems and related subjects University of Tokyo, October 23, 2013 Integrability of spectrum of N=4 SYM theory Vladimir Kazakov (ENS, Paris) Collaborations
More informationHigher-Spin Black Holes and Generalised FZZ Duality
Higher-Spin Black Holes and Generalised FZZ Duality Batsheva de Rothschild Seminar on Innovative Aspects of String Theory, Ein Bokek, Israel, 28 February 2006 Based on: Anindya Mukherjee, SM and Ari Pakman,
More informationString / gauge theory duality and ferromagnetic spin chains
String / gauge theory duality and ferromagnetic spin chains M. Kruczenski Princeton Univ. In collaboration w/ Rob Myers, David Mateos, David Winters Arkady Tseytlin, Anton Ryzhov Summary Introduction mesons,,...
More informationPlanar diagrams in light-cone gauge
Planar diagrams in light-cone gauge M. Kruczenski Purdue University Based on: hep-th/0603202 Summary Introduction Motivation: large-n, D-branes, AdS/CFT, results D-brane interactions: lowest order, light-cone
More informationScaling dimensions at small spin
Princeton Center for Theoretical Science Princeton University March 2, 2012 Great Lakes String Conference, Purdue University arxiv:1109.3154 Spectral problem and AdS/CFT correspondence Spectral problem
More informationRigid Holography and 6d N=(2,0) Theories on AdS 5 xs 1
Rigid Holography and 6d N=(2,0) Theories on AdS 5 xs 1 Ofer Aharony Weizmann Institute of Science 8 th Crete Regional Meeting on String Theory, Nafplion, July 9, 2015 OA, Berkooz, Rey, 1501.02904 Outline
More informationY-system for the Spectrum of Planar AdS/CFT: News and Checks
-,,,,, Y-system for the Spectrum of Planar AdS/CFT: News and Checks Vladimir Kazakov (ENS, Paris) Collaborations with N.Gromov, A.Kozak, S.Leurent, Z.Tsuboi and P.Vieira Outline Integrability for QFT in
More informationExact spectral equations in planar N=4 SYM theory
Euler Symposium on Theoretical and Mathematical Physics Euler International Mathematical Institute, St. Petersburg, July 12-17, 2013 Exact spectral equations in planar N=4 SYM theory Vladimir Kazakov (ENS,
More informationProgress in understanding quantum spectrum of AdS 5 S 5 superstring
Progress in understanding quantum spectrum of AdS 5 S 5 superstring Arkady Tseytlin R. Roiban, AT, arxiv:0906.494, arxiv:0.09 M. Beccaria, S. Giombi, G. Macorini, R. Roiban, AT, arxiv:03.570 M. Beccaria,
More informationRenormalisation Group Flows in Four Dimensions and the a-theorem
Renormalisation Group Flows in Four Dimensions and the a-theorem John Cardy University of Oxford Oxford, January 2012 Renormalisation Group The RG, as applied to fluctuating systems extended in space or
More informationBogolyubov Limit of Bethe Ansatz. and Dark Solitons
Bogolyubov Limit of Bethe Ansatz and Dark Solitons Konstantin Zarembo (LPT) arxiv:0702:???? Journées de la FRIF, 1.02.2008 Large-N expansion of YM theory String theory AdS/CFT correspondence Maldacena
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 informationConformal Fishnet Theory in Four Dimensions as Integrable Non-Compact Spin Chain
Workshop: Exactly Solvable Quantum Chains International Institute of Physics, Natal, 25 Juin 2018 Conformal Fishnet Theory in Four Dimensions as Integrable Non-Compact Spin Chain Vladimir Kazakov Ecole
More informationQuantum Field Theory. Kerson Huang. Second, Revised, and Enlarged Edition WILEY- VCH. From Operators to Path Integrals
Kerson Huang Quantum Field Theory From Operators to Path Integrals Second, Revised, and Enlarged Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA I vh Contents Preface XIII 1 Introducing Quantum Fields
More informationStrings, D-Branes and Gauge Theories Igor Klebanov Department of Physics Princeton University Talk at the AEI Integrability Workshop July 24, 2006
Strings, D-BranesD and Gauge Theories Igor Klebanov Department of Physics Princeton University Talk at the AEI Integrability Workshop July 24, 2006 QCD and string theory At short distances, must smaller
More informationTOPIC V BLACK HOLES IN STRING THEORY
TOPIC V BLACK HOLES IN STRING THEORY Lecture notes Making black holes How should we make a black hole in string theory? A black hole forms when a large amount of mass is collected together. In classical
More informationEmergent Quantum Criticality
(Non-)Fermi Liquids and Emergent Quantum Criticality from gravity Hong Liu Massachusetts setts Institute te of Technology HL, John McGreevy, David Vegh, 0903.2477 Tom Faulkner, HL, JM, DV, to appear Sung-Sik
More informationNon-relativistic AdS/CFT
Non-relativistic AdS/CFT Christopher Herzog Princeton October 2008 References D. T. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry, Phys. Rev. D 78,
More informationNon-Supersymmetric Seiberg duality Beyond the Planar Limit
Non-Supersymmetric Seiberg duality Beyond the Planar Limit Input from non-critical string theory, IAP Large N@Swansea, July 2009 A. Armoni, D.I., G. Moraitis and V. Niarchos, arxiv:0801.0762 Introduction
More informationShort spinning strings and AdS 5 S 5 spectrum
Short spinning strings and AdS 5 S 5 spectrum Arkady Tseytlin R. Roiban, AT, arxiv:0906.4294, arxiv:02.209 M. Beccaria, S. Giombi, G. Macorini, R. Roiban, AT, arxiv:203.570 70-s: origin of string theory
More informationA Solvable Irrelevant
A Solvable Irrelevant Deformation of AdS $ / CFT * A. Giveon, N. Itzhaki, DK arxiv: 1701.05576 + to appear Strings 2017, Tel Aviv Introduction QFT is usually thought of as an RG flow connecting a UV fixed
More informationString/gauge theory duality and QCD
String/gauge theory duality and QCD M. Kruczenski Purdue University ASU 009 Summary Introduction String theory Gauge/string theory duality. AdS/CFT correspondence. Mesons in AdS/CFT Chiral symmetry breaking
More informationChern-Simons Theories and AdS/CFT
Chern-Simons Theories and AdS/CFT Igor Klebanov PCTS and Department of Physics Talk at the AdS/CMT Mini-program KITP, July 2009 Introduction Recent progress has led to realization that coincident membranes
More information5. a d*, Entanglement entropy and Beyond
Motivation: role of higher curvature interactions on AdS/CFT calculations Overview: 1. Introductory remarks on c-theorem and CFT s 2. Holographic c-theorem I: Einstein gravity 3. Holographic c-theorem
More informationThomas Klose Uppsala University J u n e, S t r i n g s , U p p s a l a
Thomas Klose Uppsala University 2 7. J u n e, S t r i n g s 2 0 1 1, U p p s a l a The space-time dependence of two- and three-point functions of Scalar Conformal Primary Operators is fixed by conformal
More informationLecture II: Owe Philipsen. The ideal gas on the lattice. QCD in the static and chiral limit. The strong coupling expansion at finite temperature
Lattice QCD, Hadron Structure and Hadronic Matter Dubna, August/September 2014 Lecture II: Owe Philipsen The ideal gas on the lattice QCD in the static and chiral limit The strong coupling expansion at
More informationAdS/CFT duality, spin chains and 2d effective actions
AdS/CFT duality, spin chains and 2d effective actions R. Roiban, A. Tirziu and A. A. Tseytlin Asymptotic Bethe ansatz S-matrix and Landau-Lifshitz type effective 2-d actions, hep-th/0604199 also talks
More informationNew Phenomena in 2d String Theory
New Phenomena in 2d String Theory Nathan Seiberg Rutgers 2005 N.S. hep-th/0502156 J.L. Davis, F. Larsen, N.S. hep-th/0505081, and to appear J. Maldacena, N.S. hep-th/0506141 1 Low Dimensional String Theories
More informationHOLOGRAPHIC RECIPE FOR TYPE-B WEYL ANOMALIES
HOLOGRAPHIC RECIPE FOR TYPE-B WEYL ANOMALIES Danilo E. Díaz (UNAB-Talcahuano) joint work with F. Bugini (acknowledge useful conversations with R. Aros, A. Montecinos, R. Olea, S. Theisen,...) 5TH COSMOCONCE
More informationIf I only had a Brane
If I only had a Brane A Story about Gravity and QCD. on 20 slides and in 40 minutes. AdS/CFT correspondence = Anti de Sitter / Conformal field theory correspondence. Chapter 1: String Theory in a nutshell.
More informationIntegrability and Finite Size Effects of (AdS 5 /CFT 4 ) β
Integrability and Finite Size Effects of (AdS 5 /CFT 4 ) β Based on arxiv:1201.2635v1 and on-going work With C. Ahn, D. Bombardelli and B-H. Lee February 21, 2012 Table of contents 1 One parameter generalization
More informationConformal bootstrap at large charge
Conformal bootstrap at large charge Daniel L. Jafferis Harvard University 20 Years Later: The Many Faces of AdS/CFT Princeton Nov 3, 2017 DLJ, Baur Mukhametzhanov, Sasha Zhiboedov Exploring heavy operators
More informationHamiltonian approach to Yang- Mills Theories in 2+1 Dimensions: Glueball and Meson Mass Spectra
Hamiltonian approach to Yang- Mills Theories in 2+1 Dimensions: Glueball and Meson Mass Spectra Aleksandr Yelnikov Virginia Tech based on hep-th/0512200 hep-th/0604060 with Rob Leigh and Djordje Minic
More information2nd Asia-Pacific Summer School in Mathematical Physics, Canberra
1. Wrapping effect 2. Thermodynamic Bethe ansatz method 3. Luscher corrections 4. Y-systems High-order Feynman diagrams connect operators farther away When the length of a composite operator is shorter
More informationPutting String Theory to the Test with AdS/CFT
Putting String Theory to the Test with AdS/CFT Leopoldo A. Pando Zayas University of Iowa Department Colloquium L = 1 4g 2 Ga µνg a µν + j G a µν = µ A a ν ν A a µ + if a bc Ab µa c ν, D µ = µ + it a
More informationSolving the AdS/CFT Y-system
Solving the AdS/CFT Y-system Dmytro Volin Nordita, Stockholm IHP, 2011 1110.0562 N.Gromov, V.Kazakov, S.Leurent. D.V. Setup: = IIB, AdS 5 xs 5 0 This is a talk about the spectral problem: Conformal dimension
More informationApplications of AdS/CFT correspondence to cold atom physics
Applications of AdS/CFT correspondence to cold atom physics Sergej Moroz in collaboration with Carlos Fuertes ITP, Heidelberg Outline Basics of AdS/CFT correspondence Schrödinger group and correlation
More informationEric Perlmutter, DAMTP, Cambridge
Eric Perlmutter, DAMTP, Cambridge Based on work with: P. Kraus; T. Prochazka, J. Raeymaekers ; E. Hijano, P. Kraus; M. Gaberdiel, K. Jin TAMU Workshop, Holography and its applications, April 10, 2013 1.
More informationSeiberg Duality: SUSY QCD
Seiberg Duality: SUSY QCD Outline: SYM for F N In this lecture we begin the study of SUSY SU(N) Yang-Mills theory with F N flavors. This setting is very rich! Higlights of the next few lectures: The IR
More informationSpiky strings, light-like Wilson loops and a pp-wave anomaly
Spiky strings, light-like Wilson loops and a pp-wave anomaly M. Kruczenski Purdue University Based on: arxiv:080.039 A. Tseytlin, M.K. arxiv:0804.3438 R. Ishizeki, A. Tirziu, M.K. Summary Introduction
More informationHamiltonian approach to Yang- Mills Theories in 2+1 Dimensions: Glueball and Meson Mass Spectra
Hamiltonian approach to Yang- Mills Theories in 2+1 Dimensions: Glueball and Meson Mass Spectra Aleksandr Yelnikov Virginia Tech based on hep-th/0512200 hep-th/0604060 with Rob Leigh and Djordje Minic
More informationN=4 Super-Yang-Mills in t Hooft limit as Exactly Solvable 4D Conformal Field Theory
PACIFIC 2014 UCLA Symposium on Particle Astrophysics and Cosmology Including Fundamental Interactions September 15-20, 2014, Moorea, French Polynesia N=4 Super-Yang-Mills in t Hooft limit as Exactly Solvable
More informationThree-Charge Black Holes and ¼ BPS States in Little String Theory
Three-Charge Black Holes and ¼ BPS States in Little String Theory SUNGJAY LEE KOREA INSTITUTE FOR ADVANCED STUDIES Joint work (JHEP 1512, 145) with Amit Giveon, Jeff Harvey, David Kutasov East Asia Joint
More informationIntroduction to AdS/CFT
Introduction to AdS/CFT Who? From? Where? When? Nina Miekley University of Würzburg Young Scientists Workshop 2017 July 17, 2017 (Figure by Stan Brodsky) Intuitive motivation What is meant by holography?
More informationSphere Partition Functions, Topology, the Zamolodchikov Metric
Sphere Partition Functions, Topology, the Zamolodchikov Metric, and Extremal Correlators Weizmann Institute of Science Efrat Gerchkovitz, Jaume Gomis, ZK [1405.7271] Jaume Gomis, Po-Shen Hsin, ZK, Adam
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 informationInverse square potential, scale anomaly, and complex extension
Inverse square potential, scale anomaly, and complex extension Sergej Moroz Seattle, February 2010 Work in collaboration with Richard Schmidt ITP, Heidelberg Outline Introduction and motivation Functional
More information!onformali" Los# J.-W. Lee D. T. Son M. Stephanov D.B.K. arxiv: Phys.Rev.D80:125005,2009
!onformali" Los# J.-W. Lee D. T. Son M. Stephanov D.B.K arxiv:0905.4752 Phys.Rev.D80:125005,2009 Motivation: QCD at LARGE N c and N f Colors Flavors Motivation: QCD at LARGE N c and N f Colors Flavors
More informationHigher Spin AdS/CFT at One Loop
Higher Spin AdS/CFT at One Loop Simone Giombi Higher Spin Theories Workshop Penn State U., Aug. 28 2015 Based mainly on: SG, I. Klebanov, arxiv: 1308.2337 SG, I. Klebanov, B. Safdi, arxiv: 1401.0825 SG,
More informationTechniques for exact calculations in 4D SUSY gauge theories
Techniques for exact calculations in 4D SUSY gauge theories Takuya Okuda University of Tokyo, Komaba 6th Asian Winter School on Strings, Particles and Cosmology 1 First lecture Motivations for studying
More informationEffective Field Theory in Cosmology
C.P. Burgess Effective Field Theory in Cosmology Clues for cosmology from fundamental physics Outline Motivation and Overview Effective field theories throughout physics Decoupling and naturalness issues
More informationChiral Symmetry Breaking from Intersecting D-Branes
EFI-06-18 arxiv:hep-th/0608177v1 5 Aug 006 Chiral Symmetry Breaking from Intersecting D-Branes E. Antonyan, J. A. Harvey and D. Kutasov EFI and Department of Physics, University of Chicago 5640 S. Ellis
More informationCFTs with O(N) and Sp(N) Symmetry and Higher Spins in (A)dS Space
CFTs with O(N) and Sp(N) Symmetry and Higher Spins in (A)dS Space Igor Klebanov Talk at New England Strings Meeting Brown University November 6, 2015 Based mainly on L. Fei, S. Giombi, IK, arxiv:1404.1094
More information8.821 F2008 Lecture 05
8.821 F2008 Lecture 05 Lecturer: McGreevy Scribe: Evangelos Sfakianakis September 22, 2008 Today 1. Finish hindsight derivation 2. What holds up the throat? 3. Initial checks (counting of states) 4. next
More information20 Entanglement Entropy and the Renormalization Group
20 Entanglement Entropy and the Renormalization Group Entanglement entropy is very di cult to actually calculate in QFT. There are only a few cases where it can be done. So what is it good for? One answer
More informationPerturbative Integrability of large Matrix Theories
35 th summer institute @ ENS Perturbative Integrability of large Matrix Theories August 9 th, 2005 Thomas Klose Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute), Potsdam, Germany
More informationScaling and integrability from AdS 5 S 5
Scaling and integrability from AdS 5 S 5 Riccardo Ricci Imperial College London DAMTP Cambridge 14th October Work in collaboration with S. Giombi, R.Roiban, A. Tseytlin and C.Vergu Outline Introduction
More informationBubbling Geometries for Half BPS Wilson Lines. Satoshi Yamaguchi (IHES) S. Yamaguchi, hep-th/ S. Yamaguchi, to appear
Bubbling Geometries for Half BPS Wilson Lines Satoshi Yamaguchi (IHES) S. Yamaguchi, hep-th/0601089 S. Yamaguchi, to appear 1. Overview AdS5 CFT4 AdS5 x S5 Goal deform Supergravity Solutions 4dim N=4 Super
More informationP-ADIC STRINGS AT FINITE TEMPERATURE
P-ADIC STRINGS AT FINITE TEMPERATURE Jose A. R. Cembranos Work in collaboration with Joseph I. Kapusta and Thirthabir Biswas T. Biswas, J. Cembranos, J. Kapusta, PRL104:021601 (2010) T. Biswas, J. Cembranos,
More informationQuark-gluon plasma from AdS/CFT Correspondence
Quark-gluon plasma from AdS/CFT Correspondence Yi-Ming Zhong Graduate Seminar Department of physics and Astronomy SUNY Stony Brook November 1st, 2010 Yi-Ming Zhong (SUNY Stony Brook) QGP from AdS/CFT Correspondence
More informationQGP, Hydrodynamics and the AdS/CFT correspondence
QGP, Hydrodynamics and the AdS/CFT correspondence Adrián Soto Stony Brook University October 25th 2010 Adrián Soto (Stony Brook University) QGP, Hydrodynamics and AdS/CFT October 25th 2010 1 / 18 Outline
More informationClassical AdS String Dynamics. In collaboration with Ines Aniceto, Kewang Jin
Classical AdS String Dynamics In collaboration with Ines Aniceto, Kewang Jin Outline The polygon problem Classical string solutions: spiky strings Spikes as sinh-gordon solitons AdS string ti as a σ-model
More informationQuantum Fields in Curved Spacetime
Quantum Fields in Curved Spacetime Lecture 3 Finn Larsen Michigan Center for Theoretical Physics Yerevan, August 22, 2016. Recap AdS 3 is an instructive application of quantum fields in curved space. The
More informationNikolay Gromov. Based on
Nikolay Gromov Based on N. G., V.Kazakov, S.Leurent, D.Volin 1305.1939,????.???? N. G., F. Levkovich-Maslyuk, G. Sizov, S.Valatka????.???? A. Cavaglia, D. Fioravanti, N.G, R.Tateo????.???? December, 2013
More information8.821 String Theory Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.821 String Theory Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 8.821 F2008 Lecture 04 Lecturer: McGreevy
More informationString theory effects on 5D black strings
String theory effects on 5D black strings Alejandra Castro University of Michigan Work in collaboration with J. Davis, P. Kraus and F. Larsen hep-th/0702072, hep-th/0703087, 0705.1847[hep-th], 0801.1863
More information8.821 String Theory Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.821 String Theory Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 8.821 F2008 Lecture 02: String theory
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 informationMarta Orselli. Based on: hep-th/ , hep-th/ hep-th/ , arxiv: arxiv: , arxiv: work in progress
Marta Orselli Based on: hep-th/0605234, hep-th/0608115 hep-th/0611242, arxiv:0707.1621 arxiv:0806.3370, arxiv:0912.5522 + work in progress IDEA: obtain an understanding of the quantum mechanical nature
More informationOn higher-spin gravity in three dimensions
On higher-spin gravity in three dimensions Jena, 6 November 2015 Stefan Fredenhagen Humboldt-Universität zu Berlin und Max-Planck-Institut für Gravitationsphysik Higher spins Gauge theories are a success
More informationNon-relativistic holography
University of Amsterdam AdS/CMT, Imperial College, January 2011 Why non-relativistic holography? Gauge/gravity dualities have become an important new tool in extracting strong coupling physics. The best
More informationA New Regulariation of N = 4 Super Yang-Mills Theory
A New Regulariation of N = 4 Super Yang-Mills Theory Humboldt Universität zu Berlin Institut für Physik 10.07.2009 F. Alday, J. Henn, J. Plefka and T. Schuster, arxiv:0908.0684 Outline 1 Motivation Why
More informationThemodynamics at strong coupling from Holographic QCD
Themodynamics at strong coupling from Holographic QCD p. 1 Themodynamics at strong coupling from Holographic QCD Francesco Nitti APC, U. Paris VII Excited QCD Les Houches, February 23 2011 Work with E.
More informationFOLLOWING PINO - THROUGH THE CUSPS AND BEYOND THE PLANAR LANDS. Lorenzo Magnea. University of Torino - INFN Torino. Pino Day, Cortona, 29/05/12
FOLLOWING PINO - THROUGH THE CUSPS AND BEYOND THE PLANAR LANDS Lorenzo Magnea University of Torino - INFN Torino Pino Day, Cortona, 29/05/12 Outline Crossing paths with Pino Cusps, Wilson lines and Factorization
More informationLarge spin systematics in CFT
University of Oxford Holography, Strings and Higher Spins at Swansea with A. Bissi and T. Lukowski Introduction The problem In this talk we will consider operators with higher spin: T rϕ µ1 µl ϕ, T rϕϕ
More informationLIBERATION ON THE WALLS IN GAUGE THEORIES AND ANTI-FERROMAGNETS
LIBERATION ON THE WALLS IN GAUGE THEORIES AND ANTI-FERROMAGNETS Tin Sulejmanpasic North Carolina State University Erich Poppitz, Mohamed Anber, TS Phys.Rev. D92 (2015) 2, 021701 and with Anders Sandvik,
More informationExact results for Wilson loops in N = 4 SYM
Exact results for Wilson loops in N = 4 SYM Diego H. Correa Universidad Nacional de La Plata - CONICET - Argentina Based on arxives: 1202.4455, 1203.1019 and 1203.1913 In collaboration with: J. Henn, J.
More informationString hypothesis and mirror TBA Excited states TBA: CDT Critical values of g Konishi at five loops Summary. The Mirror TBA
The Mirror TBA Through the Looking-Glass, and, What Alice Found There Gleb Arutyunov Institute for Theoretical Physics, Utrecht University Lorentz Center, Leiden, 12 April 2010 Summary of the mirror TBA
More informationHolographic Wilsonian Renormalization Group
Holographic Wilsonian Renormalization Group JiYoung Kim May 0, 207 Abstract Strongly coupled systems are difficult to study because the perturbation of the systems does not work with strong couplings.
More informationExact Solutions of 2d Supersymmetric gauge theories
Exact Solutions of 2d Supersymmetric gauge theories Abhijit Gadde, IAS w. Sergei Gukov and Pavel Putrov UV to IR Physics at long distances can be strikingly different from the physics at short distances
More informationFour-point functions in the AdS/CFT correspondence: Old and new facts. Emery Sokatchev
Four-point functions in the AdS/CFT correspondence: Old and new facts Emery Sokatchev Laboratoire d Annecy-le-Vieux de Physique Théorique LAPTH Annecy, France 1 I. The early AdS/CFT correspondence The
More informationHeterotic Torsional Backgrounds, from Supergravity to CFT
Heterotic Torsional Backgrounds, from Supergravity to CFT IAP, Université Pierre et Marie Curie Eurostrings@Madrid, June 2010 L.Carlevaro, D.I. and M. Petropoulos, arxiv:0812.3391 L.Carlevaro and D.I.,
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 informationDuality and Emergent Gravity in AdS/CFT
Duality and Emergent Gravity in AdS/CFT Sebastian de Haro University of Amsterdam and University of Cambridge Equivalent Theories in Science and Metaphysics Princeton, 21 March 2015 Motivating thoughts
More information