Abstract
We examine the double-trace spectrum of \( \mathcal{N}=4 \) super Yang-Mills theory in the supergravity limit. At large N double-trace operators exhibit degeneracy. By considering free-field and tree-level supergravity contributions to four-point functions of half-BPS operators we resolve the degeneracy for a large family of double-trace operators. The mixing problem reveals a surprisingly simple structure which allows us to obtain their three-point functions at leading order in the large N expansion as well as their leading anomalous dimensions.
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J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].
A.L. Fitzpatrick, E. Katz, D. Poland and D. Simmons-Duffin, Effective Conformal Theory and the Flat-Space Limit of AdS, JHEP 07 (2011) 023 [arXiv:1007.2412] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju and B.C. van Rees, A Natural Language for AdS/CFT Correlators, JHEP 11 (2011) 095 [arXiv:1107.1499] [INSPIRE].
Z. Komargodski and A. Zhiboedov, Convexity and liberation at large spin, JHEP 11 (2013) 140 [arXiv:1212.4103] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, The Analytic Bootstrap and AdS Superhorizon Locality, JHEP 12 (2013) 004 [arXiv:1212.3616] [INSPIRE].
L.F. Alday, A. Bissi and T. Lukowski, Lessons from crossing symmetry at large-N , JHEP 06 (2015) 074 [arXiv:1410.4717] [INSPIRE].
C. Beem, L. Rastelli and B.C. van Rees, More \( \mathcal{N}=4 \) superconformal bootstrap, Phys. Rev. D 96 (2017) 046014 [arXiv:1612.02363] [INSPIRE].
O. Aharony, L.F. Alday, A. Bissi and E. Perlmutter, Loops in AdS from conformal field theory, JHEP 07 (2017) 036 [arXiv:1612.03891] [INSPIRE].
L.F. Alday, A. Bissi and E. Perlmutter, Holographic reconstruction of AdS exchanges from crossing symmetry, JHEP 08 (2017) 147 [arXiv:1705.02318] [INSPIRE].
L. Rastelli and X. Zhou, Mellin amplitudes for AdS 5 × S 5, Phys. Rev. Lett. 118 (2017) 091602 [arXiv:1608.06624] [INSPIRE].
H. Liu and A.A. Tseytlin, On four point functions in the CFT/AdS correspondence, Phys. Rev. D 59 (1999) 086002 [hep-th/9807097] [INSPIRE].
E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Graviton exchange and complete four point functions in the AdS/CFT correspondence, Nucl. Phys. B 562 (1999) 353 [hep-th/9903196] [INSPIRE].
G. Arutyunov and S. Frolov, Scalar quartic couplings in type IIB supergravity on AdS 5 × S 5, Nucl. Phys. B 579 (2000) 117 [hep-th/9912210] [INSPIRE].
G. Arutyunov and S. Frolov, Four point functions of lowest weight CPOs in N = 4 SYM(4) in supergravity approximation, Phys. Rev. D 62 (2000) 064016 [hep-th/0002170] [INSPIRE].
G. Arutyunov, F.A. Dolan, H. Osborn and E. Sokatchev, Correlation functions and massive Kaluza-Klein modes in the AdS/CFT correspondence, Nucl. Phys. B 665 (2003) 273 [hep-th/0212116] [INSPIRE].
G. Arutyunov and E. Sokatchev, On a large-N degeneracy in N = 4 SYM and the AdS/CFT correspondence, Nucl. Phys. B 663 (2003) 163 [hep-th/0301058] [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].
L. Berdichevsky and P. Naaijkens, Four-point functions of different-weight operators in the AdS/CFT correspondence, JHEP 01 (2008) 071 [arXiv:0709.1365] [INSPIRE].
L.I. Uruchurtu, Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence, JHEP 03 (2009) 133 [arXiv:0811.2320] [INSPIRE].
L.I. Uruchurtu, Next-next-to-extremal four point functions of N = 4 1/2 BPS operators in the AdS/CFT correspondence, JHEP 08 (2011) 133 [arXiv:1106.0630] [INSPIRE].
G. Arutyunov, S. Frolov, R. Klabbers and S. Savin, Towards 4-point correlation functions of any \( \frac{1}{2} \) -BPS operators from supergravity, JHEP 04 (2017) 005 [arXiv:1701.00998] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [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].
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].
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, Conformal partial wave expansions for N = 4 chiral four point functions, Annals Phys. 321 (2006) 581 [hep-th/0412335] [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].
E. D’Hoker et al., Extremal correlators in the AdS/CFT correspondence, in The many faces of the superworld, M.A. Shifman ed., World Sicentific, Singapore (2000), hep-th/9908160 [INSPIRE].
C. Rayson, Some aspects of conformal \( \mathcal{N}=4 \) SYM four point function, arXiv:1706.04450 [INSPIRE].
L.F. Alday and A. Bissi, Loop corrections to supergravity on AdS 5 × S 5, 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, JHEP 01 (2018) 035 [arXiv:1706.02822] [INSPIRE].
L.F. Alday, Large spin perturbation theory for conformal field theories, Phys. Rev. Lett. 119 (2017) 111601 [arXiv:1611.01500] [INSPIRE].
H.J. Kim, L.J. Romans and P. van Nieuwenhuizen, The mass spectrum of chiral N = 2 D = 10 supergravity on S 5,Phys. Rev. D 32 (1985) 389 [INSPIRE].
B. Eden, P.S. Howe, C. Schubert, E. Sokatchev and P.C. West, Four point functions in N = 4 supersymmetric Yang-Mills theory at two loops, Nucl. Phys. B 557 (1999) 355 [hep-th/9811172] [INSPIRE].
B. Eden, C. Schubert and E. Sokatchev, Three loop four point correlator in N = 4 SYM, Phys. Lett. B 482 (2000) 309 [hep-th/0003096] [INSPIRE].
B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Hidden symmetry of four-point correlation functions and amplitudes in N = 4 SYM, Nucl. Phys. B 862 (2012) 193 [arXiv:1108.3557] [INSPIRE].
B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N = 4 SYM, Nucl. Phys. B 862 (2012) 450 [arXiv:1201.5329] [INSPIRE].
J. Drummond et al., Leading singularities and off-shell conformal integrals, JHEP 08 (2013) 133 [arXiv:1303.6909] [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, JHEP 08 (2016) 053 [arXiv:1512.02926] [INSPIRE].
J.L. Bourjaily, P. Heslop and V.-V. Tran, Perturbation theory at eight loops: novel structures and the breakdown of manifest conformality in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 116 (2016) 191602 [arXiv:1512.07912] [INSPIRE].
J.L. Bourjaily, P. Heslop and V.-V. Tran, Amplitudes and correlators to ten loops using simple, graphical bootstraps, JHEP 11 (2016) 125 [arXiv:1609.00007] [INSPIRE].
B. Eden, A.C. Petkou, C. Schubert and E. Sokatchev, Partial nonrenormalization of the stress tensor four point function in N = 4 SYM and AdS/CFT, Nucl. Phys. B 607 (2001) 191 [hep-th/0009106] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, On loop corrections to string theory effective actions, Nucl. Phys. B 298 (1988) 109 [INSPIRE].
M. Nirschl and H. Osborn, Superconformal Ward identities and their solution, Nucl. Phys. B 711 (2005) 409 [hep-th/0407060] [INSPIRE].
N.I. Usyukina and A.I. Davydychev, An approach to the evaluation of three and four point ladder diagrams, Phys. Lett. B 298 (1993) 363 [INSPIRE].
L. Andrianopoli and S. Ferrara, On short and long SU(2, 2/4) multiplets in the AdS/CFT correspondence, Lett. Math. Phys. 48 (1999) 145 [hep-th/9812067] [INSPIRE].
P.J. Heslop, Superfield representations of superconformal groups, Class. Quant. Grav. 19 (2002) 303 [hep-th/0108235] [INSPIRE].
P.J. Heslop and P.S. Howe, Four point functions in N = 4 SYM, JHEP 01 (2003) 043 [hep-th/0211252] [INSPIRE].
A. Bissi and T. Łukowski, Revisiting \( \mathcal{N}=4 \) superconformal blocks, JHEP 02 (2016) 115 [arXiv:1508.02391] [INSPIRE].
R. Doobary and P. Heslop, Superconformal partial waves in Grassmannian field theories, JHEP 12 (2015) 159 [arXiv:1508.03611] [INSPIRE].
G. Arutyunov, S. Frolov and A.C. Petkou, Operator product expansion of the lowest weight CPOs in \( \mathcal{N}=4 \) SYM 4 at strong coupling, Nucl. Phys. B 586 (2000) 547 [Erratum ibid. B 609 (2001) 539] [hep-th/0005182] [INSPIRE].
P.J. Heslop and P.S. Howe, OPEs and three-point correlators of protected operators in N = 4 SYM, Nucl. Phys. B 626 (2002) 265 [hep-th/0107212] [INSPIRE].
P.J. Heslop and P.S. Howe, Aspects of N = 4 SYM, JHEP 01 (2004) 058 [hep-th/0307210] [INSPIRE].
V.K. Dobrev and V.B. Petkova, All positive energy unitary irreducible representations of extended conformal supersymmetry, Phys. Lett. 162B (1985) 127 [INSPIRE].
M. Bianchi, B. Eden, G. Rossi and Y.S. Stanev, On operator mixing in N = 4 SYM, Nucl. Phys. B 646 (2002) 69 [hep-th/0205321] [INSPIRE].
L.F. Alday and J.M. Maldacena, Comments on operators with large spin, JHEP 11 (2007) 019 [arXiv:0708.0672] [INSPIRE].
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Aprile, F., Drummond, J., Heslop, P. et al. Unmixing supergravity. J. High Energ. Phys. 2018, 133 (2018). https://doi.org/10.1007/JHEP02(2018)133
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DOI: https://doi.org/10.1007/JHEP02(2018)133