Integrability for the Full Spectrum of Planar AdS/CFT Nikolay Gromov DESY/HU/PNPI V.Kazakov and P.Vieira.

Slides:

Advertisements

Similar presentations

Hirota integrable dynamics: from quantum spin chains to AdS/CFT integrability Vladimir Kazakov (ENS, Paris) International Symposium Ahrenshoop “Recent.

Advertisements

Integrability in the Multi-Regge Regime Volker Schomerus DESY Hamburg Based on work w. Jochen Bartels, Jan Kotanski, Martin Sprenger, Andrej Kormilitzin,

On d=3 Yang-Mills-Chern- Simons theories with “fractional branes” and their gravity duals Ofer Aharony Weizmann Institute of Science 14 th Itzykson Meeting.

Summing planar diagrams

Yerevan State University / Leibniz Universität Hannover Supersymmetry in Integrable Systems - SIS'10 International Workshop, August 2010, Yerevan,

On correlation functions and anomalous dimensions of planar N=4 SYM theory: twist-2 operators and BFKL Vladimir Kazakov (ENS,Paris) “CFT and Integrability”

The quark-antiquark potential in N=4 Super Yang Mills Juan Maldacena Based on: arXiv: , arXiv: , arXiv: N =4 super Yang Mills,

Giant Magnon and Spike Solutions in String Theories Bum-Hoon Lee Center for Quantum SpaceTime(CQUeST)/Physics Dept. Sogang University, Seoul, Korea PAQFT08,

The Giant Magnon and Spike Solution Chanyong Park (CQUeST) Haengdang Workshop ’07, The Giant Magnon and Spike Solution Chanyong Park.

Chanyong Park 35 th Johns Hopkins Workshop ( Budapest, June 2011 ) Based on Phys. Rev. D 83, (2011) arXiv : arXiv :

Semi-Classical strings as probes of AdS/CFT M. Kruczenski Purdue University Based on: arXiv: R. Roiban, A. Tirziu, A. Tseytlin, M.K. arXiv:

Spin Chain in Gauge Theory and Holography Yong-Shi Wu Department of Physics, University of Utah, Center for Advanced Study, Tsinghua University, and Shanghai.

Spiky strings, light-like Wilson loops and a pp-wave anomaly M. Kruczenski Purdue University Based on: arXiv: arXiv: A. Tseytlin, M.K.

Strings in AdS pp-waves M. Kruczenski Purdue University Based on: arXiv: arXiv: A. Tseytlin, M.K. arXiv: arXiv: R. Ishizeki,

Large spin operators in string/gauge theory duality M. Kruczenski Purdue University Based on: arXiv: (L. Freyhult, A. Tirziu, M.K.) Miami 2009.

Bethe Ansatz in the AdS/CFT correspondence Konstantin Zarembo (Uppsala U.) EuroStrings 2006 Cambridge, 4/4/06 Thanks to: Niklas Beisert (Princeton) Johan.

Yangian Symmetry in Yang-Mills Theories S. G. Rajeev Seminar at Cornell University Dec 8 th 2004.

Spiky Strings in the SL(2) Bethe Ansatz

A window into 4D integrability: the exact spectrum of N = 4 SYM from Y-system Vladimir Kazakov (ENS,Paris) “Great Lakes Strings” Conference 2011 Chicago.

Spiky Strings and Giant Magnons on S 5 M. Kruczenski Purdue University Based on: hep-th/ (Russo, Tseytlin, M.K.)

Strings in AdS pp-waves M. Kruczenski Purdue University Based on: arXiv: A. Tseytlin, M.K. arXiv: R. Ishizeki, A. Tirziu, M.K. + work.

String / gauge theory duality and ferromagnetic spin chains Rob Myers, David Mateos, David Winters Arkady Tseytlin, Anton Ryzhov M. Kruczenski Princeton.

Excited QCD 2010, February 3 (Tatra National Park, 2010) Holographic Models for Planar QCD without AdS/CFT Correspondence Sergey Afonin Ruhr-University.

Status of Spectral Problem in planar N=4 SYM Vladimir Kazakov (ENS,Paris) Collaborations with: Nikolay Gromov (King’s College, London) Sebastien Leurent.

Nikolay Gromov Based on N. G., V. Kazakov, S. Leurent, D. Volin , N. G., F. Levkovich-Maslyuk, G. Sizov, S. Valatka A. Cavaglia,

Integrability and Bethe Ansatz in the AdS/CFT correspondence Konstantin Zarembo (Uppsala U.) Nordic Network Meeting Helsinki, Thanks to: Niklas.

Nikolay Gromov Based on works with V.Kazakov, S.Leurent, D.Volin F. Levkovich-Maslyuk, G. Sizov Nikolay Gromov Based on works with.

Bethe Ansatz and Integrability in AdS/CFT correspondence Konstantin Zarembo (Uppsala U.) “Constituents, Fundamental Forces and Symmetries of the Universe”,

Different faces of integrability in the gauge theories or in hunting for the symmetries Isaac Newton Institute, October 8.

Integrability in Superconformal Chern-Simons Theories Konstantin Zarembo Ecole Normale Supérieure “Symposium on Theoretical and Mathematical Physics”,

Solving the spectral AdS/CFT Y-system Vladimir Kazakov (ENS,Paris) “ Maths of Gauge and String Theory” London, 5/05/2012 Collaborations with Gromov, Leurent,

Exploring TBA in the mirror AdS 5 × S 5 Ryo Suzuki School of Mathematics, Trinity College Dublin Ryo Suzuki School of Mathematics, Trinity College Dublin.

PRIN meeting - Pisa, 17/5/2013 S. Penati 1 A Survey in ABJM: Scattering Amplitudes and Wilson loops Silvia Penati University of Milano-Bicocca and INFN.

Exact Results for perturbative partition functions of theories with SU(2|4) symmetry Shinji Shimasaki (Kyoto University) JHEP1302, 148 (2013) (arXiv: [hep-th])

Super Yang Mills Scattering amplitudes at strong coupling Juan Maldacena Based on L. Alday & JM arXiv: [hep-th] & to appear Strings 2007, Madrid.

Integrability of N=6 Super Chern-Simons Theories Dongsu Bak University of Seoul with S. J. Rey and D. Kang (KIAS, 9/24/2008) TexPoint fonts used in EMF.

Nikolay Gromov Based on N. G., V. Kazakov, S. Leurent, D. Volin , N. G., F. Levkovich-Maslyuk, G. Sizov, S. Valatka A. Cavaglia,

Gauge Theory, Superstrings and Supermagnets Volker Schomerus SYSY Goettingen 2012.

Finite N Index and Angular Momentum Bound from Gravity “KEK Theory Workshop 2007” Yu Nakayama, 13 th. Mar (University of Tokyo) Based on hep-th/

1 Integrability in AdS^5 x S_5 string theory: general 1-loop results Based on [N.G., Pedro Vieira] hep-th/ , hep-th/ , to appear.

World-sheet Scattering in AdS 5 xS 5 Konstantin Zarembo (Uppsala U.) Random Matrix Theory: Recent Applications, Copenhagen, T.Klose, T.McLoughlin,

Bethe ansatz in String Theory Konstantin Zarembo (Uppsala U.) Integrable Models and Applications, Lyon,

Cambridge, Dec 10th, 2007 Thomas Klose Princeton Center for Theoretical Physics based on work with Valentina Giangreco Puletti and Olof Ohlson Sax: hep-th/

Minkyoo Kim (Wigner Research Centre for Physics) 9th, September, 2013 Seminar in KIAS.

Dressing factor in integrable AdS/CFT system Dmytro Volin Annecy, 15 April 2010 x x x x x x x x x x x x 2g - 2g x x x x x x x x x x arXiv: arXiv:

Multi-Loop Miracles in N=4 Super-Yang-Mills Theory Z. Bern, L.D., V. Smirnov, hep-th/ F. Cachazo, M. Spradlin, A. Volovich, hep-th/ Z. Bern,

Numerical Solution of the Spectral Problem and BFKL at Next-to-Next-to-Leading Order in N=4 SYM Fedor Levkovich-Maslyuk King’s College London based on.

Infinite dimensional symmetries in the AdS/CFT correspondence Io Kawaguchi Particle Physics Group, Department of Physics, Kyoto University GCOE Symposium.

Gauge Theories, D-Branes and Strings Gauge Theories, D-Branes and Strings Igor Klebanov Department of Physics Talk at Jefferson Lab November 16, 2007.

Bethe Ansatz in AdS/CFT: from local operators to classical strings Konstantin Zarembo (Uppsala U.) J. Minahan, K. Z., hep-th/ N. Beisert, J. Minahan,

Two scalar fields of the N=4 SYM theory: Long local operators: Can be mapped to the spin chain states: The mixing matrix is an integrable spin chain.

Integrability and Bethe Ansatz in the AdS/CFT correspondence Konstantin Zarembo (Uppsala U.) Nordic Network Meeting Helsinki, Thanks to: Niklas.

Minimal surfaces in AdS 5, Wilson loops and Amplitudes Juan Maldacena.

Heidelberg, June 2008 Volker Schomerus - DESY Hamburg - Of Mesons and Metals – Bethe & the 5th Dimension.

Finite Volume Spectrum of 2D Field Theories from Hirota Dynamics Vladimir Kazakov (ENS,Paris) Conference in honor of Kenzo Ishikawa and Noboru Kawamoto.

Relating e+e- annihilation to high energy scattering at weak and strong coupling Yoshitaka Hatta (U. Tsukuba) JHEP 11 (2008) 057; arXiv: [hep-ph]

Integrability and AdS/CFT correspondence in three dimensions Konstantin Zarembo École Normale Supérieure Paris “Sakharov Conference”, Moscow,

Bethe Ansatz in AdS/CFT Correspondence Konstantin Zarembo (Uppsala U.) J. Minahan, K. Z., hep-th/ N. Beisert, J. Minahan, M. Staudacher, K. Z.,

B.-H.L, R. Nayak, K. Panigrahi, C. Park On the giant magnon and spike solutions for strings on AdS(3) x S**3. JHEP 0806:065,2008. arXiv: J. Kluson,

Why Y? Exploiting the Hirota Integrable Dynamics of AdS/CFT Vladimir Kazakov (ENS, Paris) « Integrability in Gauge and String Theory » NORDITA, Stockholm,

Nikolay Gromov Based on works with V.Kazakov, S.Leurent, D.Volin F. Levkovich-Maslyuk, G. Sizov Nikolay Gromov Based on works with.

Nikolay Gromov Based on works with V.Kazakov, P.Vieira & A.Kozak Nikolay Gromov Based on works with V.Kazakov, P.Vieira & A.Kozak Symposium on Theoretical.

Vladimir Kazakov (ENS,Paris)

Gauge/String Duality and Integrable Systems

Integrable Open Spin Chains from Flavored ABJM Theory

T. McLoughlin, J. Minahan, R. Roiban, K. Zarembo

Quantum properties of supersymmetric gauge theories

Conformal Fishnet Theory

Paths into Multi-Regge Regions

Correlators in N=4 SYM via QSC

Presentation transcript:

Integrability for the Full Spectrum of Planar AdS/CFT Nikolay Gromov DESY/HU/PNPI V.Kazakov and P.Vieira

Motivation Spectrum of an interacting field theory is a funny problem by itself Some quantities are shared with realistic QCD We can test string/gauge duality

N=4 Supersymmetric Yang-Mills Theory The action: Field content:

YM: Local operators and spin chains - Dilatation operator – integrable Hamiltonian

The spectrum Ground state: Excited states (magnons):

periodicity condition: momentum scattering phase shifts periodicity of wave function ©Zarembo

7 2) Get eigenvalues 1) Solve polynomial equation YM: One-loop - Integrable Hamiltonian Lepatov Faddeev, Korchemsky Minahan, Zarembo

8 Numerical Solution Till Bargheer, Niklas Beisert, N. G.

String theory

(type IIB super ) string theory in AdS 5 xS 5 x is dual to a 4 dimensional conformal field theory (N=4 SYM) Local operators String states Maldacena AdS/CFT Duality Anomalous dimensions Spectrum

x String tension`t Hooft coupling String couplingNumber of colors AdS/CFT Duality Summetry:

Beisert, Staudacher; Beisert,Eden,Staudacher Bethe equations

Vacuum I.e. from the asymptotical spectrum (R=\infty) we can compute the Ground state energy for ANY finite volume!

SO(4) Symmetry: Анзац Бетэ: Zamolodchikov x2 Faddeev, Reshetikhin

Ground state from ABA The typical configuration of roots is We define: Saddle point equation:

Above ground state Dorey, Totteo, Bazhanov

Spectrum of SO(4)

AdS/CFT Generalization N.G., Kazakov, Vieira

Large L limit Use Hirota equation:

20 S-matrix Obeys Yang-Baxter: Then (see lectures of Faddeev hep-th/ ): SU(2|2) invariant tensor with 4 fundamental indeses The eigevalues solves hirota!

Konishi operator For weak coupling constant: The simplest operator In agreement with perturbation theory!! 4-loops! Kotikov, Lipatov, Rej, Staudacher and Velizhanin Sieg, Torrielli Janik, Bojnok, N.G., Kazakov, Vieira

CP3xAdS4 / N=6 Chern- Simons N.G., Kazakov, Vieira Aharony, Bergman, Jafferis and Maldacena

Conclusions We can go below BAE now Integrability allows to predict very complicated perturbative calculations It is possible to compute some quantities for arbitrary coupling QCD BFKL could be checked