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

Slides:



Advertisements
Similar presentations
1 Holographic description of Hadrons from String Theory Shigeki Sugimoto (IPMU) Rencontres de Moriond, March 25, La Thuile, Italy (based on works.
Advertisements

Analysis of QCD via Supergravity S. Sugimoto (YITP) based on hep-th/ (T. Ibaraki + S.S.) Windows to new paradigm in particle Sendai.
Martín Schvellinger Instituto de Física de La Plata - CONICET Departamento de Física - UNLP The gauge/gravity duality and Non-Relativistic Quantum Field.
Baryons with Holography Hideo SUGANUMA ( Kyoto Univ. ) Toru KOJO ( Kyoto Univ. ) Kanabu NAWA ( RCNP ) in collaboration with.
Spectroscopy of fermionic operators in AdS/CFT with flavor Ingo Kirsch Workshop „QCD and String Theory“ Ringberg Castle, Tegernsee, July 2-8, 2006 I. K.,
Summing planar diagrams
N =4 Supersymmetric Gauge Theory, Twistor Space, and Dualities David A. Kosower Saclay Lectures Fall Term 2004.
Euclidean Wilson loops and Riemann theta functions M. Kruczenski Purdue University Based on: arXiv: (w/ R. Ishizeki, S. Ziama) Great Lakes 2011.
Gauge/Gravity Duality 2 Prof Nick Evans AdS/CFT Correspondence TODAY Quarks Deforming AdS Confinement Chiral Symmetry Breaking LATER Other brane games.
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:
3rd International Workshop On High Energy Physics In The LHC Era.
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.
Shock waves in strongly coupled plasmas M. Kruczenski Purdue University Based on: arXiv: (S. Khlebnikov, G. Michalogiorgakis, M.K.) Quantum Gravity.
Functional renormalization – concepts and prospects.
String/gauge theory duality and QCD M. Kruczenski Purdue University ASU 2009.
QCD – from the vacuum to high temperature an analytical approach an analytical approach.
Large N c QCD Towards a Holographic Dual of David Mateos Perimeter Institute ECT, Trento, July 2004.
Spiky Strings in the SL(2) Bethe Ansatz
Spin chains and strings in Y p,q and L p,q|r manifolds Martin Kruczenski Princeton University Based on hep-th/ and hep-th/ w/ S. Benvenuti.
Planar diagrams in light-cone gauge hep-th/ M. Kruczenski Purdue University Based on:
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.
Excited QCD 2010, February 3 (Tatra National Park, 2010) Holographic Models for Planar QCD without AdS/CFT Correspondence Sergey Afonin Ruhr-University.
Field Theory: The Past 25 Years Nathan Seiberg (IAS) The Future of Physics October, 2004 A celebration of 25 Years of.
Integrability and Bethe Ansatz in the AdS/CFT correspondence Konstantin Zarembo (Uppsala U.) Nordic Network Meeting Helsinki, Thanks to: Niklas.
Jet quenching at RHIC and LHC from finite endpoint momentum strings Andrej Ficnar Columbia University Hard Probes 2013 November 5, 2013 Andrej Ficnar,
Holographic Description of Quantum Black Hole on a Computer Yoshifumi Hyakutake (Ibaraki Univ.) Collaboration with M. Hanada ( YITP, Kyoto ), G. Ishiki.
Gauge Theory, Superstrings and Supermagnets Volker Schomerus SYSY Goettingen 2012.
The Hierarchy Problem and New Dimensions at a Millimeter Ye Li Graduate Student UW - Madison.
Holographic model for hadrons in deformed AdS 5 background K. Ghoroku (Fukuoka Tech.) N. Maru (U. Rome) M. Yahiro (Kyushu U.) M. Tachibana (Saga U.) Phys.Lett.B633(2006)606.
Multi-quark potential from AdS/QCD based on arXiv: Wen-Yu Wen Lattice QCD.
Quantum Gravity As an Ordinary Gauge Theory Juan Maldacena Institute for Advanced Study Princeton, New Jersey.
5d truncation ignoring the 5-sphere (SO(6) gauge symmetry) There are 42 scalars - a 20 of SO(6) - a 10 and 10 of SO(6) - scalar dilaton-axion, singlets.
WHAT BREAKS ELECTROWEAK SYMMETRY ?. We shall find the answer in experiments at the LHC? Most likely it will tells us a lot about the physics beyond the.
Light quark jet quenching in AdS/CFT Andrej Ficnar Columbia University Hot Quarks 2012 October 15, 2012.
Bethe ansatz in String Theory Konstantin Zarembo (Uppsala U.) Integrable Models and Applications, Lyon,
II Russian-Spanish Congress “Particle and Nuclear Physics at all scales and Cosmology”, Saint Petersburg, Oct. 4, 2013 RECENT ADVANCES IN THE BOTTOM-UP.
The fast life of holographic mesons Aninda Sinha Perimeter Institute, Canada. with Robert Myers arXiv:0802.nnnn Quark Matter 2008, Jaipur, India.
Wilson Loops in AdS/CFT M. Kruczenski Purdue University Miami Based on work in collaboration with Arkady Tseytlin (Imperial College). To appear.
1 Lattice Quantum Chromodynamics 1- Literature : Lattice QCD, C. Davis Hep-ph/ Burcham and Jobes By Leila Joulaeizadeh 19 Oct
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.
Time Dependent Quark Masses and Big Bang Nucleosynthesis Myung-Ki Cheoun, G. Mathews, T. Kajino, M. Kusagabe Soongsil University, Korea Asian Pacific Few.
Strings, Gravity and the Large N Limit of Gauge Theories Juan Maldacena Institute for Advanced Study Princeton, New Jersey.
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,
Holographic Hadrons in dense medium Sang-Jin Sin
Predictions by string theory? f 0 (1500) → 4π 0 : Suppressed Charge radius of Roper = 0.73[fm] [w/ C.I.Tan and S.Terashima, ] [w/ T.Sakai and.
Integrability for the Full Spectrum of Planar AdS/CFT Nikolay Gromov DESY/HU/PNPI V.Kazakov and P.Vieira.
Integrability and Bethe Ansatz in the AdS/CFT correspondence Konstantin Zarembo (Uppsala U.) Nordic Network Meeting Helsinki, Thanks to: Niklas.
Gauge/Gravity Duality Prof Nick Evans Big picture – slides Key computations - board TODAY Introduction Strings & Branes AdS/CFT Correspondence QCD-like.
Heidelberg, June 2008 Volker Schomerus - DESY Hamburg - Of Mesons and Metals – Bethe & the 5th Dimension.
알기 쉬운 초끈 이론 박 재모 (Postech). Outline 1. Partcle physics 2. Black holes 3. String theory 4. M theory 5. D branes 6. Gauge/Gravity theory correspondence.
Hadrons in a Dynamical AdS/QCD model Colaborators: W de Paula (ITA), K Fornazier (ITA), M Beyer (Rostock), H Forkel (Berlin) Tobias Frederico Instituto.
A nonperturbative definition of N=4 Super Yang-Mills by the plane wave matrix model Shinji Shimasaki (Osaka U.) In collaboration with T. Ishii (Osaka U.),
Hadrons from a hard wall AdS/QCD model Ulugbek Yakhshiev (Inha University & National University of Uzbekistan) Collaboration Hyun-Chul Kim (Inha University)
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,
Semiclassical correlation functions in holography Kostya Zarembo “Strings, Gauge Theory and the LHC”, Copenhagen, K.Z.,
Nikolay Gromov Based on works with V.Kazakov, S.Leurent, D.Volin F. Levkovich-Maslyuk, G. Sizov Nikolay Gromov Based on works with.
Gauge/String Duality and Integrable Systems
Andrej Ficnar Columbia University
Ziqiang Zhang Huazhong Normal University
Double Heavy Hadronic Spectrum from Supersymmetric LFHQCD
Jun Nishimura (KEK, SOKENDAI) JLQCD Collaboration:
EMERGENT CLASSICAL STRINGS
Presentation transcript:

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

Summary ● Introduction mesons String picture π, ρ,... Quark model Fund. strings ( Susy, 10d, Q.G. ) QCD Large N-limit Effective strings qq Strong coupling q

AdS/CFT N = 4 SYM II B on AdS 5 xS 5 S 5 : X 1 2 +X 2 2 +…X 6 2 = R 2 AdS 5 : Y 1 2 +Y 2 2 +…-Y 5 2 -Y 6 2 =-R 2 AdS/CFT Known examples QCD deformStrings?

● Add quarks We get models where the spectrum of qq bound states can be computed in the strong coupling regime ● Strings from gauge theory Problem: Compute scaling dimension (or energy) of states of a large number of particles in N =4 SYM Equivalent to solving Heisenberg spin chain (Minahan and Zarembo). Use effective action for spin waves: is the same as the string action AdS/CFT predicts!.

Introduction String theory ●) Quantum field theory: Relativistic theory of point particles ●) String theory: Relativistic theory of extended objects: Strings Why? Original motivation: Phenomenological model for hadrons (proton, neutron,pions, rho, etc.)

Regge trajectories Simple model of rotating strings gives Strings thought as fundamental improvement m m M 2 (GeV) 2 J ρ5ρ5 ρ3ρ3 ρ a2a2 a4a4 a6a6

Theoretical problems Tachyons Taking care by supersymmetry Quantum mechanically consistent only in 10 dim. Unified models? Including gravity 5 types of strings

What about hadrons? Instead: bound states of quarks. mesons: qq baryons: qqq Interactions: SU(3); q = ; A μ = quarks gluons Coupling constant small at large energies (100 GeV) but large at small energies. No expansion parameter. Confinement V=- k/r V=k r (color) electric flux=string?

Idea (‘t Hooft) Take large-N limit, q= ; A μ = fixed (‘t Hooft coupling) N N x N 1/N: perturbative parameter. Planar diagrams dominate (sphere) Next: 1/N 2 corrections (torus) + 1/N 4 (2-handles) + … Looks like a string theory Can be a way to derive a string descriptions of mesons

AdS/CFT correspondence (Maldacena) Gives a precise example of the relation between strings and gauge theory. Gauge theory N = 4 SYM SU(N) on R 4 A μ, Φ i, Ψ a Operators w/ conf. dim. String theory IIB on AdS 5 xS 5 radius R String states w/ fixed λ large → string th. λ small → field th.

Mesons (w/ D. Mateos, R. Myers, D. Winters) We need quarks (following Karch and Katz) D-brane 3+1 bdy z=0 z q q q q bound state=string So, in AdS/CFT, a meson is a string rotating in 5 dim.!

Meson spectrum ( N = 4 is conformal → Coulomb force) 2m q Regge Coulomb The cases J=0, ½, 1 are special, very light, namely “tightly bound”. (E b ~ 2 m q ) (numerical result)

For J=0,1/2,1 we can compute the exact spectrum (in ‘t Hooft limit and at strong coupling) 2 scalars (M/M 0 ) 2 = (n+m+1) (n+m+2), m ≥ 0 1 scalar (M/M 0 ) 2 = (n+m+1) (n+m+2), m ≥ 1 1 scalar (M/M 0 ) 2 = (n+m+2) (n+m+3), m ≥ 1 1 scalar (M/M 0 ) 2 = (n+m) (n+m+1), m ≥ 1 1 vector (M/M 0 ) 2 = (n+m+1) (n+m+2), m ≥ 0 1 fermion (M/M 0 ) 2 = (n+m+1) (n+m+2), m ≥ 0 1 fermion (M/M 0 ) 2 = (n+m+2) (n+m+3), m ≥ 0 n ≥ 0 ; there is a mass gap of order M 0 for m q ≠0

Confining case (w/ D. Mateos, R. Myers, D. Winters) Add quarks to Witten’s confining bkg. ● Spectrum is numerical ● For m q =0 there is a massless meson Φ. (M Φ =0) Goldstone boson of chiral symmetry breaking ● For m q ≠ 0 GMOR- relation ● Rot. String (w/ Vaman, Pando-Zayas, Sonnenschein) reproduces “improved model”: m m

We can compute meson spectrum at strong coupling. In the confining case results are similar to QCD. How close are we to QCD? Ideal sit.In practice E E 5-dim 4-dim mesons glueballs 5-dim 4-dim M KK Λ QCD quarks gluons confinement dim. red.

Can we derive the string picture from the field theory? (PRL 93 (2004) M.K.) Study known case: N = 4 SYM Take two scalars X = Φ 1 + i Φ 2 ; Y= Φ 3 + i Φ 4 O = Tr(XX…Y..Y…X), J 1 X’s, J 2 Y’s, J 1 +J 2 large Compute 1-loop conformal dimension of O, or equiv. compute energy of a bound state of J 1 particles of type X and J 2 of type Y (but on a three sphere) R 4 S 3 xR Δ E

Large number of ops. (or states). All permutations of Xs and Ys mix so we have to diag. a huge matrix. Nice idea (Minahan-Zarembo). Relate to a phys. system Tr( X X…Y X X Y ) | ↑ ↑…↓ ↑ ↑ ↓ › operator conf. of spin chain mixing matrix op. on spin chain Ferromagnetic Heisenberg model !

Ground state (s) | ↑ ↑ … ↑ ↑ ↑ ↑ › Tr( X X … X X X X ) | ↓ ↓ … ↓ ↓ ↓ ↓ › Tr( Y Y … Y Y Y Y ) First excited states More generic (low energy) states: Spin waves l (BMN)

Other states, e.g. with J 1 =J 2 Spin waves of long wave-length have low energy and are described by an effective action in terms of two angles θ, φ: direction in which the spin points. Taking J large with λ/J 2 fixed: classical solutions

According to AdS/CFT there is a string description particle: X(t) string: X(σ,t) We need S 3 : X 1 2 +X 2 2 +X 3 2 +X 4 2 = R 2 J 1 J 2 CM: J 1 Rot: J 2 Action: S[ θ(σ,t), φ(σ,t) ], which, for large J is: (agrees w/ f.t.)

Suggests that ( θ, φ ) = ( θ, φ) namely that ‹ S › is the position of the string Examples | ↑ ↑ … ↑ ↑ ↑ ↑ › point-like

Strings as bound states Fields create particles: X | x , Y | y  Q.M. : |  = cos(  /2) exp(i  /2 ) |x  + sin(  /2) exp(- i  /2) |y  We consider a state with a large number of particles i=1…J each in a state v i = |  (  i,  i ) . (Coherent state) Can be thought as created by O = Tr (v 1 v 2 v 3 … v n )

Strings are useful to describe states of a large number of particles (in the large–N limit) | x  | y 

Extension to higher orders in the field theory: O(λ 2 ) We need H (Beisert et al.) At next order we get second neighbors interactions

We have to define the effective action more precisely n1n1 n4n4 n2n2 n5n5 n3n3 nini …… Look for states |  such that From those, find |  such that =minimum

After doing the calculation we get: (Ryzhov, Tseytlin, M.K.) Agrees with string theory!

Rotation in AdS 5 ? (Gubser, Klebanov, Polyakov) θ = ω t

Verification using Wilson loops (MK, Makeenko) The anomalous dimensions of twist two operators can also be computed by using the cusp anomaly of light-like Wilson loops (Korchemsky and Marchesini). In AdS/CFT Wilson loops can be computed using surfaces of minimal area in AdS 5 (Maldacena, Rey, Yee) z The result agrees with the rotating string calculation.

Generalization to higher twist operators (MK)

Conclusions AdS/CFT provides a unique possibility of analytically understanding the low energy limit of non-abelian gauge theories (confinement) Two results: ● Computed the masses of quark / anti-quark bound states at strong coupling. ● Showed a way in which strings directly emerge from the gauge theory.