Abstract
Gravitational shockwaves are insensitive to higher-curvature corrections in the action. Recent work found that the OPE coefficients of lowest-twist multi-stress-tensor operators, computed holographically in a planar black hole background, are insensitive as well. In this paper, we analyze the relation between these two limits. We explicitly evaluate the two-point function on a shockwave background to all orders in a large central charge expansion. In the geodesic limit, we find that the ANEC exponentiates in the multi-stress-tensor sector. To compare with the black hole limit, we obtain a recursion relation for the lowest-twist products of two stress tensors in a spherical black hole background, letting us efficiently compute their OPE coefficients and prove their insensitivity to higher curvature terms. After resumming the lowest-twist stress-tensors and analytically continuing their contributions to the Regge limit, we find a perfect agreement with the shockwave computation. We also discuss the role of double-trace operators, global degenerate states, and multi-stress-tensor conformal blocks. These holographic results suggest the existence of a larger universal structure in higher-dimensional CFTs.
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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].
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality constraints on corrections to the graviton three-point coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
N. Afkhami-Jeddi, T. Hartman, S. Kundu and A. Tajdini, Einstein gravity 3-point functions from conformal field theory, JHEP 12 (2017) 049 [arXiv:1610.09378] [INSPIRE].
M. Kulaxizi, A. Parnachev and A. Zhiboedov, Bulk phase shift, CFT Regge limit and Einstein gravity, JHEP 06 (2018) 121 [arXiv:1705.02934] [INSPIRE].
D. Li, D. Meltzer and D. Poland, Conformal bootstrap in the Regge limit, JHEP 12 (2017) 013 [arXiv:1705.03453] [INSPIRE].
N. Afkhami-Jeddi, T. Hartman, S. Kundu and A. Tajdini, Shockwaves from the operator product expansion, JHEP 03 (2019) 201 [arXiv:1709.03597] [INSPIRE].
D. Meltzer and E. Perlmutter, Beyond a = c: gravitational couplings to matter and the stress tensor OPE, JHEP 07 (2018) 157 [arXiv:1712.04861] [INSPIRE].
N. Afkhami-Jeddi, S. Kundu and A. Tajdini, A bound on massive higher spin particles, JHEP 04 (2019) 056 [arXiv:1811.01952] [INSPIRE].
A.L. Fitzpatrick and K.-W. Huang, Universal lowest-twist in CFTs from holography, JHEP 08 (2019) 138 [arXiv:1903.05306] [INSPIRE].
G.T. Horowitz and N. Itzhaki, Black holes, shock waves and causality in the AdS/CFT correspondence, JHEP 02 (1999) 010 [hep-th/9901012] [INSPIRE].
R. Karlsson, M. Kulaxizi, A. Parnachev and P. Tadić, Black holes and conformal Regge bootstrap, JHEP 10 (2019) 046 [arXiv:1904.00060] [INSPIRE].
Y.-Z. Li, Z.-F. Mai and H. Lü, Holographic OPE coefficients from AdS black holes with matters, JHEP 09 (2019) 001 [arXiv:1905.09302] [INSPIRE].
M. Kulaxizi, G.S. Ng and A. Parnachev, Subleading eikonal, AdS/CFT and double stress tensors, JHEP 10 (2019) 107 [arXiv:1907.00867] [INSPIRE].
M.S. Costa, J. Drummond, V. Goncalves and J. Penedones, The role of leading twist operators in the Regge and Lorentzian OPE limits, JHEP 04 (2014) 094 [arXiv:1311.4886] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, D. Li and J. Wang, On information loss in AdS3/CFT2 , JHEP 05 (2016) 109 [arXiv:1603.08925] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan and M.T. Walters, Virasoro conformal blocks and thermality from classical background fields, JHEP 11 (2015) 200 [arXiv:1501.05315] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan and M.T. Walters, Universality of long-distance AdS physics from the CFT bootstrap, JHEP 08 (2014) 145 [arXiv:1403.6829] [INSPIRE].
H. Chen, C. Hussong, J. Kaplan and D. Li, A numerical approach to Virasoro blocks and the information paradox, JHEP 09 (2017) 102 [arXiv:1703.09727] [INSPIRE].
T. Hartman, Entanglement entropy at large central charge, arXiv:1303.6955 [INSPIRE].
D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect, Phys. Rev. Lett. 115 (2015) 131603 [arXiv:1412.5123] [INSPIRE].
T. Anous, T. Hartman, A. Rovai and J. Sonner, Black hole collapse in the 1/c expansion, JHEP 07 (2016) 123 [arXiv:1603.04856] [INSPIRE].
L. Cornalba, M.S. Costa, J. Penedones and R. Schiappa, Eikonal approximation in AdS/CFT: from shock waves to four-point functions, JHEP 08 (2007) 019 [hep-th/0611122] [INSPIRE].
L. Cornalba, M.S. Costa and J. Penedones, Eikonal approximation in AdS/CFT: resumming the gravitational loop expansion, JHEP 09 (2007) 037 [arXiv:0707.0120] [INSPIRE].
L. Cornalba, M.S. Costa, J. Penedones and R. Schiappa, Eikonal approximation in AdS/CFT: conformal partial waves and finite N four-point functions, Nucl. Phys. B 767 (2007) 327 [hep-th/0611123] [INSPIRE].
L. Cornalba, M.S. Costa and J. Penedones, Eikonal methods in AdS/CFT: BFKL pomeron at weak coupling, JHEP 06 (2008) 048 [arXiv:0801.3002] [INSPIRE].
D.M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].
M. Kologlu, P. Kravchuk, D. Simmons-Duffin and A. Zhiboedov, The light-ray OPE and conformal colliders, arXiv:1905.01311 [INSPIRE].
H. Chen, A.L. Fitzpatrick, J. Kaplan, D. Li and J. Wang, Degenerate operators and the 1/c expansion: Lorentzian resummations, high order computations and super-Virasoro blocks, JHEP 03 (2017) 167 [arXiv:1606.02659] [INSPIRE].
P.C. Aichelburg and R.U. Sexl, On the gravitational field of a massless particle, Gen. Rel. Grav. 2 (1971) 303 [INSPIRE].
M. Hotta and M. Tanaka, Shock wave geometry with nonvanishing cosmological constant, Class. Quant. Grav. 10 (1993) 307 [INSPIRE].
K. Sfetsos, On gravitational shock waves in curved space-times, Nucl. Phys. B 436 (1995) 721 [hep-th/9408169] [INSPIRE].
G.T. Horowitz and A.R. Steif, Space-time singularities in string theory, Phys. Rev. Lett. 64 (1990) 260 [INSPIRE].
D. Amati and C. Klimčík, Nonperturbative computation of the Weyl anomaly for a class of nontrivial backgrounds, Phys. Lett. B 219 (1989) 443 [INSPIRE].
P. Kravchuk and D. Simmons-Duffin, Light-ray operators in conformal field theory, JHEP 11 (2018) 102 [arXiv:1805.00098] [INSPIRE].
M. Henneaux and C. Teitelboim, Asymptotically anti-de Sitter spaces, Commun. Math. Phys. 98 (1985) 391 [INSPIRE].
S. Hollands, A. Ishibashi and D. Marolf, Comparison between various notions of conserved charges in asymptotically AdS-spacetimes, Class. Quant. Grav. 22 (2005) 2881 [hep-th/0503045] [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].
L. Cornalba, Eikonal methods in AdS/CFT: Regge theory and multi-reggeon exchange, arXiv:0710.5480 [INSPIRE].
M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [INSPIRE].
K.-W. Huang, Stress-tensor commutators in conformal field theories near the lightcone, Phys. Rev. D 100 (2019) 061701 [arXiv:1907.00599] [INSPIRE].
H. Casini, E. Teste and G. Torroba, Modular Hamiltonians on the null plane and the Markov property of the vacuum state, J. Phys. A 50 (2017) 364001 [arXiv:1703.10656] [INSPIRE].
C. Córdova and S.-H. Shao, Light-ray operators and the BMS algebra, Phys. Rev. D 98 (2018) 125015 [arXiv:1810.05706] [INSPIRE].
A. Belin, D.M. Hofman and G. Mathys, Einstein gravity from ANEC correlators, JHEP 08 (2019) 032 [arXiv:1904.05892] [INSPIRE].
M. Kologlu, P. Kravchuk, D. Simmons-Duffin and A. Zhiboedov, Shocks, superconvergence and a stringy equivalence principle, arXiv:1904.05905 [INSPIRE].
S. Balakrishnan, V. Chandrasekaran, T. Faulkner, A. Levine and A. Shahbazi-Moghaddam, Entropy variations and light ray operators from replica defects, arXiv:1906.08274 [INSPIRE].
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ArXiv ePrint: 1907.10810
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Fitzpatrick, A.L., Huang, KW. & Li, D. Probing universalities in d > 2 CFTs: from black holes to shockwaves. J. High Energ. Phys. 2019, 139 (2019). https://doi.org/10.1007/JHEP11(2019)139
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DOI: https://doi.org/10.1007/JHEP11(2019)139