Abstract
We consider structure constants of single-trace operators at strong coupling in planar \( \mathcal{N} \) = 4 SYM theory using the hexagon formalism. We concentrate on heavy-heavy- light correlators where the heavy operators are BMN operators, with large R-charges and finite anomalous dimensions, and the light one is a finite-charge chiral primary operator. They describe the couplings between two highly boosted strings and a supergravity mode in the bulk dual. In the hexagon framework, two sums over virtual magnons are needed to bind the hexagons together around the light operator. We evaluate these sums explicitly at strong coupling, for a certain choice of BMN operators, and show that they factorise into a ratio of Gamma functions and a simple stringy prefactor. The former originates from giant mirror magnons scanning the AdS geometry while the latter stems from small fluctuations around the BMN vacuum. The resulting structure constants have poles at positions where an enhanced mixing with double-trace operators is expected and zeros whenever the process is forbidden by supersymmetry. We also discuss the transition to the classical regime, when the length of the light operator scales like the string tension, where we observe similitudes with the Neumann coefficients of the pp-wave String Field Theory vertex.
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References
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
G. Mack, D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary dual resonance models. Scalar amplitudes, arXiv:0907.2407 [INSPIRE].
L. Rastelli and X. Zhou, Mellin amplitudes for AdS5× S5 , Phys. Rev. Lett.118 (2017) 091602 [arXiv:1608.06624] [INSPIRE].
L.F. Alday and A. Bissi, Loop corrections to supergravity on AdS5× S5 , Phys. Rev. Lett.119 (2017) 171601 [arXiv:1706.02388] [INSPIRE].
F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Quantum gravity from conformal field theory, JHEP01 (2018) 035 [arXiv:1706.02822] [INSPIRE].
L.F. Alday and S. Caron-Huot, Gravitational S-matrix from CFT dispersion relations, JHEP12 (2018) 017 [arXiv:1711.02031] [INSPIRE].
F. Aprile, J. Drummond, P. Heslop and H. Paul, Double-trace spectrum of N = 4 supersymmetric Yang-Mills theory at strong coupling, Phys. Rev.D 98 (2018) 126008 [arXiv:1802.06889] [INSPIRE].
S. Caron-Huot and A.-K. Trinh, All tree-level correlators in AdS5× S5 supergravity: hidden ten-dimensional conformal symmetry, JHEP01 (2019) 196 [arXiv:1809.09173] [INSPIRE].
D.J. Binder, S.M. Chester, S.S. Pufu and Y. Wang, \( \mathcal{N} \) = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization, JHEP12 (2019) 119 [arXiv:1902.06263] [INSPIRE].
V. Gon¸calves, R. Pereira and X. Zhou, 20′ five-point function from AdS5× S5supergravity, JHEP10 (2019) 247 [arXiv:1906.05305] [INSPIRE].
F.A. Dolan, M. Nirschl and H. Osborn, Conjectures for large N superconformal N = 4 chiral primary four point functions, Nucl. Phys.B 749 (2006) 109 [hep-th/0601148] [INSPIRE].
F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Unmixing supergravity, JHEP02 (2018) 133 [arXiv:1706.08456] [INSPIRE].
N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys.99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
J. Escobedo, N. Gromov, A. Sever and P. Vieira, Tailoring three-point functions and integrability, JHEP09 (2011) 028 [arXiv:1012.2475] [INSPIRE].
B. Basso, A. Sever and P. Vieira, Spacetime and flux tube S-matrices at finite coupling for N = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett.111 (2013) 091602 [arXiv:1303.1396] [INSPIRE].
Z. Bajnok and R.A. Janik, String field theory vertex from integrability, JHEP04 (2015) 042 [arXiv:1501.04533] [INSPIRE].
B. Basso, S. Komatsu and P. Vieira, Structure constants and integrable bootstrap in planar N = 4 SYM theory, arXiv:1505.06745 [INSPIRE].
T. Fleury and S. Komatsu, Hexagonalization of correlation functions, JHEP01 (2017) 130 [arXiv:1611.05577] [INSPIRE].
B. Eden and A. Sfondrini, Tessellating cushions: four-point functions in \( \mathcal{N} \) = 4 SYM, JHEP10 (2017) 098 [arXiv:1611.05436] [INSPIRE].
T. Bargheer et al., Handling handles: nonplanar integrability in \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett.121 (2018) 231602 [arXiv:1711.05326] [INSPIRE].
B. Eden, Y. Jiang, D. le Plat and A. Sfondrini, Colour-dressed hexagon tessellations for correlation functions and non-planar corrections, JHEP02 (2018) 170 [arXiv:1710.10212] [INSPIRE].
R. Ben-Israel, A.G. Tumanov and A. Sever, Scattering amplitudes — Wilson loops duality for the first non-planar correction, JHEP08 (2018) 122 [arXiv:1802.09395] [INSPIRE].
K.-Y. Kim, M. Kim and K. Lee, Structure constants of a single trace operator and determinant operators from hexagon, arXiv:1906.11515 [INSPIRE].
Y. Jiang, S. Komatsu and E. Vescovi, Structure constants in \( \mathcal{N} \) = 4 SYM at finite coupling as worldsheet g-function, arXiv:1906.07733 [INSPIRE].
T. Fleury and S. Komatsu, Hexagonalization of correlation functions. Part II. two-particle contributions, JHEP02 (2018) 177 [arXiv:1711.05327] [INSPIRE].
D. Chicherin, A. Georgoudis, V. Gon¸calves and R. Pereira, All five-loop planar four-point functions of half-BPS operators in \( \mathcal{N} \) = 4 SYM, JHEP11 (2018) 069 [arXiv:1809.00551] [INSPIRE].
T. Bargheer et al., Handling handles. Part II. Stratification and data analysis, JHEP11 (2018) 095 [arXiv:1809.09145] [INSPIRE].
F. Coronado, Perturbative four-point functions in planar \( \mathcal{N} \) = 4 SYM from hexagonalization, JHEP01 (2019) 056 [arXiv:1811.00467] [INSPIRE].
F. Coronado, Bootstrapping the simplest correlator in planar \( \mathcal{N} \) = 4 SYM at all loops, arXiv:1811.03282 [INSPIRE].
I. Kostov, V.B. Petkova and D. Serban, Determinant formula for the octagon form factor in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett.122 (2019) 231601 [arXiv:1903.05038] [INSPIRE].
I. Kostov, V.B. Petkova and D. Serban, The octagon as a determinant, JHEP11 (2019) 178 [arXiv:1905.11467] [INSPIRE].
Y. Jiang, S. Komatsu, I. Kostov and D. Serban, Clustering and the three-point function, J. Phys.A 49 (2016) 454003 [arXiv:1604.03575] [INSPIRE].
Y. Kazama, S. Komatsu and T. Nishimura, Classical integrability for three-point functions: cognate structure at weak and strong couplings, JHEP10 (2016) 042 [Erratum ibid.02 (2018) 047] [arXiv:1603.03164] [INSPIRE].
Y. Kazama and S. Komatsu, Three-point functions in the rminSU (2) sector at strong coupling, JHEP03 (2014) 052 [arXiv:1312.3727] [INSPIRE].
Y. Kazama and S. Komatsu, On holographic three point functions for GKP strings from integrability, JHEP01 (2012) 110 [Erratum ibid.06 (2012) 150] [arXiv:1110.3949] [INSPIRE].
R.A. Janik and A. Wereszczynski, Correlation functions of three heavy operators: the AdS contribution, JHEP12 (2011) 095 [arXiv:1109.6262] [INSPIRE].
E.I. Buchbinder and A.A. Tseytlin, Semiclassical correlators of three states with large S5charges in string theory in AdS5× S5 , Phys. Rev.D 85 (2012) 026001 [arXiv:1110.5621] [INSPIRE].
T. Klose and T. McLoughlin, A light-cone approach to three-point functions in AdS5× S5 , JHEP04 (2012) 080 [arXiv:1106.0495] [INSPIRE].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFTd/AdSd+1correspondence, Nucl. Phys.B 546 (1999) 96 [hep-th/9804058] [INSPIRE].
E. D’Hoker et al., Extremal correlators in the AdS/CFT correspondence, hep-th/9908160 [INSPIRE].
L.F. Alday and A. Bissi, Higher-spin correlators, JHEP10 (2013) 202 [arXiv:1305.4604] [INSPIRE].
J.A. Minahan and R. Pereira, Three-point correlators from string amplitudes: mixing and Regge spins, JHEP04 (2015) 134 [arXiv:1410.4746] [INSPIRE].
G.P. Korchemsky, On level crossing in conformal field theories, JHEP03 (2016) 212 [arXiv:1512.05362] [INSPIRE].
L.F. Alday and A. Bissi, Crossing symmetry and Higher spin towers, JHEP12 (2017) 118 [arXiv:1603.05150] [INSPIRE].
B. Basso, V. Goncalves and S. Komatsu, Structure constants at wrapping order, JHEP05 (2017) 124 [arXiv:1702.02154] [INSPIRE].
B. Basso, J. Caetano and T. Fleury, Hexagons and correlators in the fishnet theory, JHEP11 (2019) 172 [arXiv:1812.09794] [INSPIRE].
Z. Bajnok and R.A. Janik, From the octagon to the SFT vertex — Gluing and multiple wrapping, JHEP06 (2017) 058 [arXiv:1704.03633] [INSPIRE].
Z. Bajnok, J. Balog, M. L´ajer and C. Wu, Field theoretical derivation of Lüscher’s formula and calculation of finite volume form factors, JHEP07 (2018) 174 [arXiv:1802.04021] [INSPIRE].
Z. Bajnok, M. Lajer, B. Szepfalvi and I. Vona, Leading exponential finite size corrections for non-diagonal form factors, JHEP07 (2019) 173 [arXiv:1904.00492] [INSPIRE].
K. Zarembo, Holographic three-point functions of semiclassical states, JHEP09 (2010) 030 [arXiv:1008.1059] [INSPIRE].
M.S. Costa, R. Monteiro, J.E. Santos and D. Zoakos, On three-point correlation functions in the gauge/gravity duality, JHEP11 (2010) 141 [arXiv:1008.1070] [INSPIRE].
Z. Bajnok, R.A. Janik and A. Wereszczyński, HHL correlators, orbit averaging and form factors, JHEP09 (2014) 050 [arXiv:1404.4556] [INSPIRE].
Z. Bajnok and R.A. Janik, Classical limit of diagonal form factors and HHL correlators, JHEP01 (2017) 063 [arXiv:1607.02830] [INSPIRE].
Z. Bajnok and R.A. Janik, The kinematical AdS5× S5Neumann coefficient, JHEP02 (2016) 138 [arXiv:1512.01471] [INSPIRE].
B. Basso et al., Asymptotic four point functions, JHEP07 (2019) 082 [arXiv:1701.04462] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept.323 (2000) 183 [hep-th/9905111] [INSPIRE].
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] [INSPIRE].
S. Dobashi and T. Yoneya, Impurity non-preserving 3-point correlators of BMN operators from PP-wave holography. I. Bosonic excitations, Nucl. Phys.B 711 (2005) 54 [hep-th/0409058] [INSPIRE].
S. Lee and R. Russo, Holographic cubic vertex in the pp-wave, Nucl. Phys.B 705 (2005) 296 [hep-th/0409261] [INSPIRE].
H. Shimada, Holography at string field theory level: conformal three point functions of BMN operators, Phys. Lett.B 647 (2007) 211 [hep-th/0410049] [INSPIRE].
S. Lee, S. Minwalla, M. Rangamani and N. Seiberg, Three point functions of chiral operators in D = 4, N = 4 SYM at large N , Adv. Theor. Math. Phys.2 (1998) 697 [hep-th/9806074] [INSPIRE].
J. Lucietti, S. Sch¨afer-Nameki and A. Sinha, On the plane wave cubic vertex, Phys. Rev.D 70 (2004) 026005 [hep-th/0402185] [INSPIRE].
Y.-H. He, J.H. Schwarz, M. Spradlin and A. Volovich, Explicit formulas for Neumann coefficients in the plane wave geometry, Phys. Rev.D 67 (2003) 086005 [hep-th/0211198] [INSPIRE].
N. Beisert, The analytic bethe ansatz for a chain with centrally extended su(2|2) symmetry, J. Stat. Mech.01 (2007) P01017 [nlin/0610017].
N. Beisert and M. Staudacher, Long-range rminP SU (2, 2|4) Bethe Ansatze for gauge theory and strings, Nucl. Phys.B 727 (2005) 1 [hep-th/0504190] [INSPIRE].
N. Beisert, The rminSU (2|2) dynamic S-matrix, Adv. Theor. Math. Phys.12 (2008) 945 [hep-th/0511082] [INSPIRE].
B. Basso, V. Goncalves, S. Komatsu and P. Vieira, Gluing hexagons at three loops, Nucl. Phys.B 907 (2016) 695 [arXiv:1510.01683] [INSPIRE].
N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech.0701 (2007) P01021 [hep-th/0610251] [INSPIRE].
G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings, JHEP10 (2004) 016 [hep-th/0406256] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Effective string theory revisited, JHEP09 (2012) 044 [arXiv:1203.1054] [INSPIRE].
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality constraints on corrections to the graviton three-point coupling, JHEP02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
D.M. Hofman and J.M. Maldacena, Giant magnons, J. Phys.A 39 (2006) 13095 [hep-th/0604135] [INSPIRE].
G. Arutyunov and S. Frolov, On string S-matrix, bound states and TBA, JHEP12 (2007) 024 [arXiv:0710.1568] [INSPIRE].
G. Arutyunov and S. Frolov, Foundations of the AdS5× S5superstring. Part I, J. Phys.A 42 (2009) 254003 [arXiv:0901.4937] [INSPIRE].
B. Eden and E. Sokatchev, On the OPE of 1/2 BPS short operators in N = 4 SCFT(4), Nucl. Phys.B 618 (2001) 259 [hep-th/0106249] [INSPIRE].
D. Chicherin, J. Drummond, P. Heslop and E. Sokatchev, All three-loop four-point correlators of half-BPS operators in planar \( \mathcal{N} \) = 4 SYM, JHEP08 (2016) 053 [arXiv:1512.02926] [INSPIRE].
F.A. Dolan and H. Osborn, On short and semi-short representations for four-dimensional superconformal symmetry, Annals Phys.307 (2003) 41 [hep-th/0209056] [INSPIRE].
F.A. Dolan and H. Osborn, Superconformal symmetry, correlation functions and the operator product expansion, Nucl. Phys.B 629 (2002) 3 [hep-th/0112251] [INSPIRE].
J. Ambjørn, R.A. Janik and C. Kristjansen, Wrapping interactions and a new source of corrections to the spin-chain/string duality, Nucl. Phys.B 736 (2006) 288 [hep-th/0510171] [INSPIRE].
Z. Bajnok and R.A. Janik, Four-loop perturbative Konishi from strings and finite size effects for multiparticle states, Nucl. Phys.B 807 (2009) 625 [arXiv:0807.0399] [INSPIRE].
J.A. Minahan, Holographic three-point functions for short operators, JHEP07 (2012) 187 [arXiv:1206.3129] [INSPIRE].
T. Bargheer, J.A. Minahan and R. Pereira, Computing three-point functions for short operators, JHEP03 (2014) 096 [arXiv:1311.7461] [INSPIRE].
B. Eden et al., Positivity of hexagon perturbation theory, JHEP11 (2018) 097 [arXiv:1806.06051] [INSPIRE].
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Basso, B., Zhong, Dl. Three-point functions at strong coupling in the BMN limit. J. High Energ. Phys. 2020, 76 (2020). https://doi.org/10.1007/JHEP04(2020)076
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DOI: https://doi.org/10.1007/JHEP04(2020)076