Semiclassical relativistic strings in $ {\mathit{AdS}}_{5}\times {S}^{5}$ and long scalar operators in $ \mathcal{N}=4$ SYM theory

Arkady A. Tseytlin

doi:10.1016/j.crhy.2004.09.009

String theory and fundamental forces/Théorie des cordes et forces fondamentales

Semiclassical relativistic strings in

{AdS}_{5} \times S^{5}

and long scalar operators in

N = 4

SYM theory
[Cordes relativistes semi-classiques dans

A d S_{5} \times S^{5}

et longs opérateurs dans la théorie de super Yang–Mills

N = 4

Présenté par : Guy Laval

Arkady A. Tseytlin ¹

¹ Physics Department, The Ohio State University, Columbus, OH43210-1106, USA

Comptes Rendus. Physique, Volume 5 (2004) no. 9-10, pp. 1049-1059.

Résumé
Abstract

Nous passons en revue les progrès récents sur les vérifications quantitatives de la dualité AdS/CFT dans le régime où les états « semiclassiques » de cordes sont du aux « longs » opérateurs scalaires de la théorie de super Yang–Mills $N = 4$ . En particulier, nous décrivons l'approche effective, dans laquelle le modèle sigma décrivant les états cohérents est montré émerger de l'action de la corde sur ${AdS}_{5} \times S^{5}$ et de l'Hamiltonien d'une chaîne de spin intégrable représentant l'opérateur de dilatation en SYM.

We review recent progress in quantitative checking of AdS/CFT duality in the sector of ‘semiclassical’ string states dual to ‘long’ scalar $N = 4$ super Yang–Mills operators. In particular, we describe the effective action approach, in which the same sigma model type action describing coherent states is shown to emerge from the ${AdS}_{5} \times S^{5}$ string action and from an integrable spin chain Hamiltonian representing the SYM dilatation operator.

Publié le : 2004-11-01

DOI : 10.1016/j.crhy.2004.09.009

Keywords: AdS/CFT duality, Super Yang–Mills operators
Mot clés : Dualité AdS/CFT, Théorie de super Yang–Mills

Affiliations des auteurs :

Arkady A. Tseytlin ¹

¹ Physics Department, The Ohio State University, Columbus, OH43210-1106, USA

@article{CRPHYS_2004__5_9-10_1049_0,
     author = {Arkady A. Tseytlin},
     title = {Semiclassical relativistic strings in $ {\mathit{AdS}}_{5}\times {S}^{5}$ and long scalar operators in $ \mathcal{N}=4$ {SYM} theory},
     journal = {Comptes Rendus. Physique},
     pages = {1049--1059},
     publisher = {Elsevier},
     volume = {5},
     number = {9-10},
     year = {2004},
     doi = {10.1016/j.crhy.2004.09.009},
     language = {en},
}

TY  - JOUR
AU  - Arkady A. Tseytlin
TI  - Semiclassical relativistic strings in $ {\mathit{AdS}}_{5}\times {S}^{5}$ and long scalar operators in $ \mathcal{N}=4$ SYM theory
JO  - Comptes Rendus. Physique
PY  - 2004
SP  - 1049
EP  - 1059
VL  - 5
IS  - 9-10
PB  - Elsevier
DO  - 10.1016/j.crhy.2004.09.009
LA  - en
ID  - CRPHYS_2004__5_9-10_1049_0
ER  -

%0 Journal Article
%A Arkady A. Tseytlin
%T Semiclassical relativistic strings in $ {\mathit{AdS}}_{5}\times {S}^{5}$ and long scalar operators in $ \mathcal{N}=4$ SYM theory
%J Comptes Rendus. Physique
%D 2004
%P 1049-1059
%V 5
%N 9-10
%I Elsevier
%R 10.1016/j.crhy.2004.09.009
%G en
%F CRPHYS_2004__5_9-10_1049_0

Arkady A. Tseytlin. Semiclassical relativistic strings in $ {\mathit{AdS}}_{5}\times {S}^{5}$ and long scalar operators in $ \mathcal{N}=4$ SYM theory. Comptes Rendus. Physique, Volume 5 (2004) no. 9-10, pp. 1049-1059. doi : 10.1016/j.crhy.2004.09.009. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2004.09.009/

Bibliographie
Cité par

[1] A.M. Polyakov Gauge fields and space–time, Int. J. Mod. Phys. A, Volume 17S1 (2002), p. 119 | arXiv

[2] D. Berenstein; J.M. Maldacena; H. Nastase Strings in flat space and pp waves from $N = 4$ super Yang–Mills, JHEP, Volume 0204 (2002), p. 013 | arXiv

[3] R.R. Metsaev; A.A. Tseytlin Type IIB superstring action in $AdS (5) \times S (5)$ background, Nucl. Phys. B, Volume 533 (1998), p. 109 | arXiv

[4] S.S. Gubser; I.R. Klebanov; A.M. Polyakov A semi-classical limit of the gauge/string correspondence, Nucl. Phys. B, Volume 636 (2002), p. 99 | arXiv

[5] R.R. Metsaev; R.R. Metsaev; A.A. Tseytlin Exactly solvable model of superstring in plane wave Ramond–Ramond background, Phys. Rev. D, Volume 625 (2002), p. 70 | arXiv

[6] S. Frolov; A.A. Tseytlin Semiclassical quantization of rotating superstring in ${AdS}_{5} \times S^{5}$ , JHEP, Volume 0206 (2002), p. 007 | arXiv

[7] A.A. Tseytlin Semiclassical quantization of superstrings: ${AdS}_{5} \times S^{5}$ and beyond, Int. J. Mod. Phys. A, Volume 18 (2003), p. 981 | arXiv

[8] A. Parnachev; A.V. Ryzhov Strings in the near plane wave background and AdS/CFT, JHEP, Volume 0210 (2002), p. 066 | arXiv

[9] C.G. Callan; H.K. Lee; T. McLoughlin; J.H. Schwarz; I. Swanson; X. Wu Quantizing string theory in $AdS (5) \times S^{5}$ : beyond the pp-wave, Nucl. Phys. B, Volume 673 (2003), p. 3 | arXiv

[10] D.J. Gross; A. Mikhailov; R. Roiban Operators with large R charge in $N = 4$ Yang–Mills theory, Ann. Phys., Volume 301 (2002), p. 31 | arXiv

[11] N. Beisert; C. Kristjansen; M. Staudacher The dilatation operator of $N = 4$ super Yang–Mills theory, Nucl. Phys. B, Volume 664 (2003), p. 131 | arXiv

[12] N. Beisert The su(2|3) dynamic spin chain | arXiv

[13] A. Santambrogio; D. Zanon Exact anomalous dimensions of $N = 4$ Yang–Mills operators with large R charge, Phys. Lett. B, Volume 545 (2002), p. 425 | arXiv

[14] I.R. Klebanov; M. Spradlin; A. Volovich New effects in gauge theory from pp-wave superstrings, Phys. Lett. B, Volume 548 (2002), p. 111 | arXiv

[15] D. Serban; M. Staudacher Planar $N = 4$ gauge theory and the Inozemtsev long range spin chain, JHEP, Volume 0406 (2004), p. 001 | arXiv

[16] N. Beisert; V. Dippel; M. Staudacher A novel long range spin chain and planar $N = 4$ super Yang–Mills | arXiv

[17] G. Arutyunov; S. Frolov; M. Staudacher Bethe ansatz for quantum strings | arXiv

[18] D.J. Gross; F. Wilczek Asymptotically free gauge theories. I, Phys. Rev. D, Volume 8 (1973), p. 3633

[19] A.V. Kotikov; L.N. Lipatov; V.N. Velizhanin Anomalous dimensions of Wilson operators in $N = 4$ SYM theory, Phys. Lett. B, Volume 557 (2003), p. 114 | arXiv

[20] A.V. Kotikov; L.N. Lipatov; A.I. Onishchenko; V.N. Velizhanin Three-loop universal anomalous dimension of the Wilson operators in $N = 4$ SUSY Yang–Mills model | arXiv

[21] S.S. Gubser; I.R. Klebanov; A.A. Tseytlin Coupling constant dependence in the thermodynamics of $N = 4$ supersymmetric Yang–Mills theory, Nucl. Phys. B, Volume 534 (1998), p. 202 | arXiv

[22] S. Frolov; A.A. Tseytlin Multi-spin string solutions in ${AdS}_{5} \times S^{5}$ , Nucl. Phys. B, Volume 668 (2003), p. 77 | arXiv

[23] S. Frolov; A.A. Tseytlin Quantizing three-spin string solution in ${AdS}_{5} \times S^{5}$ , JHEP, Volume 0307 (2003), p. 016 | arXiv

[24] S. Frolov; A.A. Tseytlin Rotating string solutions: AdS/CFT duality in non-supersymmetric sectors, Phys. Lett. B, Volume 570 (2003), p. 96 | arXiv

[25] G. Arutyunov; S. Frolov; J. Russo; A.A. Tseytlin Spinning strings in ${AdS}_{5} \times S^{5}$ and integrable systems, Nucl. Phys. B, Volume 671 (2003), p. 3 | arXiv

[26] G. Arutyunov; J. Russo; A.A. Tseytlin Spinning strings in ${AdS}_{5} \times S^{5}$ : new integrable system relations, Phys. Rev. D, Volume 69 (2004), p. 086009 | arXiv

[27] A.A. Tseytlin Spinning strings and AdS/CFT duality | arXiv

[28] J.A. Minahan; K. Zarembo The Bethe-ansatz for $N = 4$ super Yang–Mills, JHEP, Volume 0303 (2003), p. 013 | arXiv

[29] N. Beisert; J.A. Minahan; M. Staudacher; K. Zarembo Stringing spins and spinning strings, JHEP, Volume 0309 (2003), p. 010 | arXiv

[30] N. Beisert; S. Frolov; M. Staudacher; A.A. Tseytlin Precision spectroscopy of AdS/CFT, JHEP, Volume 0310 (2003), p. 037 | arXiv

[31] G. Arutyunov; M. Staudacher; G. Arutyunov; M. Staudacher Two-loop commuting charges and the string/gauge duality, JHEP, Volume 0403, 2004, p. 004 | arXiv

[32] J. Engquist; J.A. Minahan; K. Zarembo Yang–Mills duals for semiclassical strings on ${AdS}_{5} \times S^{5}$ , JHEP, Volume 0311 (2003), p. 063 | arXiv

[33] M. Kruczenski Spin chains and string theory | arXiv

[34] V.A. Kazakov; A. Marshakov; J.A. Minahan; K. Zarembo Classical/quantum integrability in AdS/CFT | arXiv

[35] M. Kruczenski; A.V. Ryzhov; A.A. Tseytlin Large spin limit of ${AdS}_{5} \times S^{5}$ string theory and low energy expansion of ferromagnetic spin chains | arXiv

[36] M. Lubcke; K. Zarembo Finite-size corrections to anomalous dimensions in $N = 4$ SYM theory, JHEP, Volume 0405 (2004), p. 049 | arXiv

[37] C. Kristjansen; L. Freyhult; C. Kristjansen; T. Mansson The circular, elliptic three spin string from the SU(3) spin chain, Phys. Lett. B, Volume 586, 2004, p. 106 | arXiv

[38] N. Beisert; M. Staudacher The $N = 4$ SYM integrable super spin chain, Nucl. Phys. B, Volume 670 (2003), p. 439 | arXiv

[39] J.A. Minahan Circular semiclassical string solutions on ${AdS}_{5} \times S^{5}$ , Nucl. Phys. B, Volume 648 (2003), p. 203 | arXiv

[40] W.M. Zhang; D.H. Feng; R. Gilmore Coherent states: theory and some applications, Rev. Mod. Phys., Volume 62 (1990), p. 867

[41] E.H. Fradkin; I. Affleck Quantum spin chains and the Haldane gap, J. Phys. C, Volume 1 (1991), p. 3047 350 p. (Frontiers in physics, 82)

[42] R. Hernandez; E. Lopez The SU(3) spin chain sigma model and string theory, JHEP, Volume 0404 (2004), p. 052 | arXiv

[43] B.J. Stefanski; A.A. Tseytlin Large spin limits of AdS/CFT and generalized Landau–Lifshitz equations, JHEP, Volume 0405 (2004), p. 042 | arXiv

[44] M. Kruczenski; A.A. Tseytlin Semiclassical relativistic strings in S5 and long coherent operators in $N = 4$ SYM theory | arXiv

[45] D. Mateos; T. Mateos; P.K. Townsend; D. Mateos; T. Mateos; P.K. Townsend More on supersymmetric tensionless rotating strings in ${AdS}_{5} \times S^{5}$ | arXiv

[46] A. Mikhailov Speeding strings, JHEP, Volume 0312 (2003), p. 058 | arXiv

[47] A. Mikhailov; A. Mikhailov Supersymmetric null-surfaces | arXiv

[48] J.A. Minahan Higher loops beyond the SU(2) sector | arXiv

[49] A.V. Ryzhov; A.A. Tseytlin Towards the exact dilatation operator of $N = 4$ super Yang–Mills theory | arXiv

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Semiclassical integrability in AdS/CFT

Konstantin Zarembo

C. R. Phys (2004)

Higher-loop integrability in $N = 4$ gauge theory

Niklas Beisert

C. R. Phys (2004)

Variations on the warped deformed conifold

Steven S. Gubser; Christopher P. Herzog; Igor R. Klebanov

C. R. Phys (2004)