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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1907.10810
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
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
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2019)139