Abstract
We explore how to compute, classically at strong coupling, correlation functions of local operators corresponding to classical spinning string states. The picture we obtain is of ‘fattened’ Witten diagrams, the evaluation of which turns out to be surprisingly subtle and requires a modification of the naive classical action due to a necessary projection onto appropriate wave functions. We examine string solutions which compute the simplest case of a two-point function and reproduce the right scaling with the anomalous dimensions corresponding to the energies of the associated spinning string solutions. We also describe, under some simplifying assumptions, how the spacetime dependence of a conformal three-point correlation function arises in this setup.
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I. Bena, J. Polchinski and R. Roiban, Hidden symmetries of the AdS 5 × S 5 superstring, Phys. Rev. D 69 (2004) 046002 [hep-th/0305116] [SPIRES].
J.A. Minahan and K. Zarembo, The Bethe-ansatz for N = 4 super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [SPIRES].
V.A. Kazakov, A. Marshakov, J.A. Minahan and K. Zarembo, Classical/quantum integrability in AdS/CFT, JHEP 05 (2004) 024 [hep-th/0402207] [SPIRES].
N. Beisert, V. Dippel and M. Staudacher, A novel long range spin chain and planar N = 4 super Yang-Mills, JHEP 07 (2004) 075 [hep-th/0405001] [SPIRES].
G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings, JHEP 10 (2004) 016 [hep-th/0406256] [SPIRES].
N. Beisert and M. Staudacher, Long-range PSU(2, 2|4) Bethe ansaetze for gauge theory and strings, Nucl. Phys. B 727 (2005) 1 [hep-th/0504190] [SPIRES].
N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [SPIRES].
R.A. Janik, The AdS 5 × S 5 superstring worldsheet S-matrix and crossing symmetry, Phys. Rev. D 73 (2006) 086006 [hep-th/0603038] [SPIRES].
N. Beisert, R. Hernandez and E. Lopez, A crossing-symmetric phase for AdS 5 × S 5 strings, JHEP 11 (2006) 070 [hep-th/0609044] [SPIRES].
N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. (2007) P01021 [hep-th/0610251] [SPIRES].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
G. Arutyunov and S. Frolov, String hypothesis for the AdS 5 × S 5 mirror, JHEP 03 (2009) 152 [arXiv:0901.1417] [SPIRES].
G. Arutyunov and S. Frolov, Thermodynamic Bethe Ansatz for the AdS 5 × S 5 Mirror Model, JHEP 05 (2009) 068 [arXiv:0903.0141] [SPIRES].
G. Arutyunov, S. Frolov and R. Suzuki, Exploring the mirror TBA, arXiv:0911.2224 [SPIRES].
N. Gromov, V. Kazakov and P. Vieira, Exact Spectrum of Anomalous Dimensions of Planar N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 103 (2009) 131601 [arXiv:0901.3753] [SPIRES].
N. Gromov, V. Kazakov, A. Kozak and P. Vieira, Exact Spectrum of Anomalous Dimensions of Planar N = 4 Supersymmetric Yang-Mills Theory: TBA and excited states, Lett. Math. Phys. 91 (2010) 265 [arXiv:0902.4458] [SPIRES].
D. Bombardelli, D. Fioravanti and R. Tateo, Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal, J. Phys. A 42 (2009) 375401 [arXiv:0902.3930] [SPIRES].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT(d)/AdS(d + 1) correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [SPIRES].
G. Arutyunov and S. Frolov, Some cubic couplings in type IIB supergravity on AdS 5 × S 5 and three-point functions in SYM(4) at large N, Phys. Rev. D 61 (2000) 064009 [hep-th/9907085] [SPIRES].
M. Bianchi, S. Kovacs, G. Rossi and Y.S. Stanev, Properties of the Konishi multiplet in N = 4 SYM theory, JHEP 05 (2001) 042 [hep-th/0104016] [SPIRES].
G. Georgiou, V.L. Gili and R. Russo, Operator mixing and three-point functions in N = 4 SYM, JHEP 10 (2009) 009 [arXiv:0907.1567] [SPIRES].
A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B 241 (1984) 333 [SPIRES].
E.S. Fradkin and M.Y. Palchik, New developments in D-dimensional conformal quantum field theory, Phys. Rept. 300 (1998) 1 [SPIRES].
S. Dobashi, H. Shimada and T. Yoneya, Holographic reformulation of string theory on AdS 5 × S 5 background in the PP-wave limit, Nucl. Phys. B 665 (2003) 94 [hep-th/0209251] [SPIRES].
T. Yoneya, What is holography in the plane-wave limit of AdS 5 /SYM(4) correspondence?, Prog. Theor. Phys. Suppl. 152 (2004) 108 [hep-th/0304183] [SPIRES].
S. Dobashi and T. Yoneya, Resolving the holography in the plane-wave limit of AdS/CFT correspondence, Nucl. Phys. B 711 (2005) 3 [hep-th/0406225] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, A semi-classical limit of the gauge/string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [SPIRES].
S. Frolov and A.A. Tseytlin, Multi-spin string solutions in AdS 5 × S 5, Nucl. Phys. B 668 (2003) 77 [hep-th/0304255] [SPIRES].
A.A. Tseytlin, Spinning strings and AdS/CFT duality, hep-th/0311139 [SPIRES].
E.I. Buchbinder, Energy-Spin Trajectories in AdS 5 xS 5 from Semiclassical Vertex Operators, 1002.1716 [SPIRES].
A.A. Tseytlin, On semiclassical approximation and spinning string vertex operators in AdS 5 × S 5, Nucl. Phys. B 664 (2003) 247 [hep-th/0304139] [SPIRES].
A.G. Cohen, G.W. Moore, P.C. Nelson and J. Polchinski, An Off-Shell Propagator for String Theory, Nucl. Phys. B 267 (1986) 143 [SPIRES].
A.V. Marshakov, The path integral representation of fermionic string propagator, Nucl. Phys. B 312 (1989) 178 [SPIRES].
A. Tsuji, Holography of Wilson loop correlator and spinning strings, Prog. Theor. Phys. 117 (2007) 557 [hep-th/0606030] [SPIRES].
K. Zarembo, Wilson loop correlator in the AdS/CFT correspondence, Phys. Lett. B 459 (1999) 527 [hep-th/9904149] [SPIRES].
G. Arutyunov, J. Russo and A.A. Tseytlin, Spinning strings in AdS 5 × S 5 : New integrable system relations, Phys. Rev. D 69 (2004) 086009 [hep-th/0311004] [SPIRES].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [SPIRES].
G. Arutyunov and S. Frolov, Uniform light-cone gauge for strings in AdS 5 × S 5 : Solving SU(1|1) sector, JHEP 01 (2006) 055 [hep-th/0510208] [SPIRES].
R. Roiban and A.A. Tseytlin, Quantum strings in AdS 5 × S 5 : strong-coupling corrections to dimension of Konishi operator, JHEP 11 (2009) 013 [arXiv:0906.4294] [SPIRES].
N. Gromov, V. Kazakov and P. Vieira, Exact AdS/CFT spectrum: Konishi dimension at any coupling, arXiv:0906.4240 [SPIRES].
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ArXiv ePrint: 1002.4613
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Janik, R.A., Surówka, P. & Wereszczyński, A. On correlation functions of operators dual to classical spinning string states. J. High Energ. Phys. 2010, 30 (2010). https://doi.org/10.1007/JHEP05(2010)030
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DOI: https://doi.org/10.1007/JHEP05(2010)030