Abstract
Asymptotic symmetries of AdS4 quantum gravity and gauge theory are derived by coupling the holographically dual CFT3 to Chern-Simons gauge theory and 3D gravity in a “probe” (large-level) limit. Despite the fact that the three-dimensional AdS4 boundary as a whole is consistent with only finite-dimensional asymptotic symmetries, given by AdS isometries, infinite-dimensional symmetries are shown to arise in circumstances where one is restricted to boundary subspaces with effectively two-dimensional geometry. A canonical example of such a restriction occurs within the 4D subregion described by a Wheeler-DeWitt wavefunctional of AdS4 quantum gravity. An AdS4 analog of Minkowski “super-rotation” asymptotic symmetry is probed by 3D Einstein gravity, yielding CFT2 structure (in a large central charge limit), via AdS3 foliation of AdS4 and the AdS3/CFT2 correspondence. The maximal asymptotic symmetry is however probed by 3D conformal gravity. Both 3D gravities have Chern-Simons formulation, manifesting their topological character. Chern-Simons structure is also shown to be emergent in the Poincare patch of AdS4, as soft/boundary limits of 4D gauge theory, rather than “put in by hand” as an external probe. This results in a finite effective Chern-Simons level. Several of the considerations of asymptotic symmetry structure are found to be simpler for AdS4 than for Mink4, such as non-zero 4D particle masses, 4D non-perturbative “hard” effects, and consistency with unitarity. The last of these in particular is greatly simplified because in some set-ups the time dimension is explicitly shared by each level of description: Lorentzian AdS4, CFT3 and CFT2. Relatedly, the CFT2 structure clarifies the sense in which the infinite asymptotic charges constitute a useful form of “hair” for black holes and other complex 4D states. An AdS4 analog of Minkowski “memory” effects is derived, but with late-time memory of earlier events being replaced by (holographic) “shadow” effects. Lessons from AdS4 provide hints for better understanding Minkowski asymptotic symmetries, the 3D structure of its soft limits, and Minkowski holography.
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References
A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448 [INSPIRE].
H. Bondi, M.G.J. van der Burg and A.W.K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
R.K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A 270 (1962) 103 [INSPIRE].
G. Barnich and C. Troessaert, Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited, Phys. Rev. Lett. 105 (2010) 111103 [arXiv:0909.2617] [INSPIRE].
A. Strominger, Asymptotic symmetries of Yang-Mills theory, JHEP 07 (2014) 151 [arXiv:1308.0589] [INSPIRE].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New symmetries of massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].
T. He, P. Mitra and A. Strominger, 2D Kac-Moody symmetry of 4D Yang-Mills theory, JHEP 10 (2016) 137 [arXiv:1503.02663] [INSPIRE].
D. Kapec, M. Pate and A. Strominger, New symmetries of QED, arXiv:1506.02906 [INSPIRE].
A. Strominger, Magnetic corrections to the soft photon theorem, Phys. Rev. Lett. 116 (2016) 031602 [arXiv:1509.00543] [INSPIRE].
A. Strominger, On BMS invariance of gravitational scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
T. He, V. Lysov, P. Mitra and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, JHEP 05 (2015) 151 [arXiv:1401.7026] [INSPIRE].
D. Kapec, V. Lysov, S. Pasterski and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity S-matrix, JHEP 08 (2014) 058 [arXiv:1406.3312] [INSPIRE].
V. Lysov, S. Pasterski and A. Strominger, Low’s subleading soft theorem as a symmetry of QED, Phys. Rev. Lett. 113 (2014) 111601 [arXiv:1407.3814] [INSPIRE].
A. Mohd, A note on asymptotic symmetries and soft-photon theorem, JHEP 02 (2015) 060 [arXiv:1412.5365] [INSPIRE].
T.T. Dumitrescu, T. He, P. Mitra and A. Strominger, Infinite-dimensional fermionic symmetry in supersymmetric gauge theories, arXiv:1511.07429 [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].
F.E. Low, Bremsstrahlung of very low-energy quanta in elementary particle collisions, Phys. Rev. 110 (1958) 974 [INSPIRE].
T.H. Burnett and N.M. Kroll, Extension of the low soft photon theorem, Phys. Rev. Lett. 20 (1968) 86 [INSPIRE].
C.D. White, Factorization properties of soft graviton amplitudes, JHEP 05 (2011) 060 [arXiv:1103.2981] [INSPIRE].
F. Cachazo and A. Strominger, Evidence for a new soft graviton theorem, arXiv:1404.4091 [INSPIRE].
L. Bieri and D. Garfinkle, An electromagnetic analogue of gravitational wave memory, Class. Quant. Grav. 30 (2013) 195009 [arXiv:1307.5098] [INSPIRE].
S. Pasterski, Asymptotic symmetries and electromagnetic memory, JHEP 09 (2017) 154 [arXiv:1505.00716] [INSPIRE].
L. Susskind, Electromagnetic memory, arXiv:1507.02584 [INSPIRE].
Y. Zeldovich and A. Polnarev, Radiation of gravitational waves by a cluster of superdense stars, Sov. Astron. 18 (1974) 17 [Astron. Zh. 51 (1974) 30].
V.B. Braginsky and K.S. Thorne, Gravitational-wave bursts with memory and experimental prospects, Nature 327 (1987) 123.
D. Christodoulou, Nonlinear nature of gravitation and gravitational wave experiments, Phys. Rev. Lett. 67 (1991) 1486 [INSPIRE].
A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
S. Pasterski, A. Strominger and A. Zhiboedov, New gravitational memories, JHEP 12 (2016) 053 [arXiv:1502.06120] [INSPIRE].
P.M. Zhang, C. Duval, G.W. Gibbons and P.A. Horvathy, Soft gravitons and the memory effect for plane gravitational waves, Phys. Rev. D 96 (2017) 064013 [arXiv:1705.01378] [INSPIRE].
P.M. Zhang, C. Duval, G.W. Gibbons and P.A. Horvathy, The memory effect for plane gravitational waves, Phys. Lett. B 772 (2017) 743 [arXiv:1704.05997] [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Soft hair on black holes, Phys. Rev. Lett. 116 (2016) 231301 [arXiv:1601.00921] [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Superrotation charge and supertranslation hair on black holes, JHEP 05 (2017) 161 [arXiv:1611.09175] [INSPIRE].
D. Carney, L. Chaurette, D. Neuenfeld and G.W. Semenoff, Infrared quantum information, Phys. Rev. Lett. 119 (2017) 180502 [arXiv:1706.03782] [INSPIRE].
A. Strominger, Black hole information revisited, arXiv:1706.07143 [INSPIRE].
D. Kapec, P. Mitra, A.-M. Raclariu and A. Strominger, 2D stress tensor for 4D gravity, Phys. Rev. Lett. 119 (2017) 121601 [arXiv:1609.00282] [INSPIRE].
C. Cheung, A. de la Fuente and R. Sundrum, 4D scattering amplitudes and asymptotic symmetries from 2D CFT, JHEP 01 (2017) 112 [arXiv:1609.00732] [INSPIRE].
J. de Boer and S.N. Solodukhin, A holographic reduction of Minkowski space-time, Nucl. Phys. B 665 (2003) 545 [hep-th/0303006] [INSPIRE].
S.N. Solodukhin, Reconstructing Minkowski space-time, IRMA Lect. Math. Theor. Phys. 8 (2005) 123 [hep-th/0405252] [INSPIRE].
Y.-T. Chien, M.D. Schwartz, D. Simmons-Duffin and I.W. Stewart, Jet physics from static charges in AdS, Phys. Rev. D 85 (2012) 045010 [arXiv:1109.6010] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries of QED and Weinberg’s soft photon theorem, JHEP 07 (2015) 115 [arXiv:1505.05346] [INSPIRE].
R.N.C. Costa, Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes, JHEP 11 (2012) 046 [arXiv:1206.3142] [INSPIRE].
E. Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].
Y. Aharonov and D. Bohm, Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115 (1959) 485 [INSPIRE].
G.W. Moore and N. Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. B 360 (1991) 362 [INSPIRE].
X.G. Wen, Non-abelian statistics in the fractional quantum Hall states, Phys. Rev. Lett. 66 (1991) 802 [INSPIRE].
R. Bousso and M. Porrati, Soft hair as a soft wig, Class. Quant. Grav. 34 (2017) 204001 [arXiv:1706.00436] [INSPIRE].
W. Donnelly and S.B. Giddings, How is quantum information localized in gravity?, Phys. Rev. D 96 (2017) 086013 [arXiv:1706.03104] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [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].
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].
J. Polchinski, Introduction to gauge/gravity duality, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 2010). String theory and its applications: from MeV to the Planck scale, Boulder CO U.S.A., 1-25 June 2010, pg. 3 [arXiv:1010.6134] [INSPIRE].
R. Sundrum, From fixed points to the fifth dimension, Phys. Rev. D 86 (2012) 085025 [arXiv:1106.4501] [INSPIRE].
J. Penedones, TASI lectures on AdS/CFT, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: new frontiers in fields and strings (TASI 2015), Boulder CO U.S.A., 1-26 June 2015, pg. 75 [arXiv:1608.04948] [INSPIRE].
A. Ashtekar and S. Das, Asymptotically anti-de Sitter space-times: conserved quantities, Class. Quant. Grav. 17 (2000) L17 [hep-th/9911230] [INSPIRE].
J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
A. Ashtekar, J. Bicak and B.G. Schmidt, Asymptotic structure of symmetry reduced general relativity, Phys. Rev. D 55 (1997) 669 [gr-qc/9608042] [INSPIRE].
G. Barnich and G. Compere, Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions, Class. Quant. Grav. 24 (2007) F15 [gr-qc/0610130] [INSPIRE].
M. Spradlin, A. Strominger and A. Volovich, Les Houches lectures on de Sitter space, in Unity from duality: gravity, gauge theory and strings. Proceedings, NATO Advanced Study Institute, Euro Summer School, 76th session, Les Houches France, 30 July-31 August 2001, pg. 423 [hep-th/0110007] [INSPIRE].
D. Anninos, G.S. Ng and A. Strominger, Asymptotic symmetries and charges in de Sitter space, Class. Quant. Grav. 28 (2011) 175019 [arXiv:1009.4730] [INSPIRE].
E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE].
S. Elitzur, G.W. Moore, A. Schwimmer and N. Seiberg, Remarks on the canonical quantization of the Chern-Simons-Witten theory, Nucl. Phys. B 326 (1989) 108 [INSPIRE].
E. Witten, On holomorphic factorization of WZW and coset models, Commun. Math. Phys. 144 (1992) 189 [INSPIRE].
S. Gukov, E. Martinec, G.W. Moore and A. Strominger, Chern-Simons gauge theory and the AdS 3 /CFT 2 correspondence, hep-th/0403225 [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Three-dimensional massive gauge theories, Phys. Rev. Lett. 48 (1982) 975 [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [Annals Phys. 281 (2000) 409] [INSPIRE].
J.H. Horne and E. Witten, Conformal gravity in three-dimensions as a gauge theory, Phys. Rev. Lett. 62 (1989) 501 [INSPIRE].
H. Afshar, B. Cvetkovic, S. Ertl, D. Grumiller and N. Johansson, Conformal Chern-Simons holography — lock, stock and barrel, Phys. Rev. D 85 (2012) 064033 [arXiv:1110.5644] [INSPIRE].
L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].
R. Emparan, G.T. Horowitz and R.C. Myers, Exact description of black holes on branes, JHEP 01 (2000) 007 [hep-th/9911043] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, D. Li and J. Wang, Exact Virasoro blocks from Wilson lines and background-independent operators, JHEP 07 (2017) 092 [arXiv:1612.06385] [INSPIRE].
A. Karch and L. Randall, Locally localized gravity, JHEP 05 (2001) 008 [hep-th/0011156] [INSPIRE].
R. Bousso and L. Randall, Holographic domains of anti-de Sitter space, JHEP 04 (2002) 057 [hep-th/0112080] [INSPIRE].
P.K. Townsend and B. Zhang, Thermodynamics of “exotic” Bañados-Teitelboim-Zanelli black holes, Phys. Rev. Lett. 110 (2013) 241302 [arXiv:1302.3874] [INSPIRE].
A. Bagchi, R. Gopakumar, I. Mandal and A. Miwa, GCA in 2d, JHEP 08 (2010) 004 [arXiv:0912.1090] [INSPIRE].
A. Bagchi, Correspondence between asymptotically flat spacetimes and nonrelativistic conformal field theories, Phys. Rev. Lett. 105 (2010) 171601 [arXiv:1006.3354] [INSPIRE].
A. Bagchi and R. Fareghbal, BMS/GCA redux: towards flatspace holography from non-relativistic symmetries, JHEP 10 (2012) 092 [arXiv:1203.5795] [INSPIRE].
G. Barnich, A. Gomberoff and H.A. Gonzalez, The flat limit of three dimensional asymptotically anti-de Sitter spacetimes, Phys. Rev. D 86 (2012) 024020 [arXiv:1204.3288] [INSPIRE].
C. Duval, G.W. Gibbons and P.A. Horvathy, Conformal Carroll groups and BMS symmetry, Class. Quant. Grav. 31 (2014) 092001 [arXiv:1402.5894] [INSPIRE].
C. Duval, G.W. Gibbons and P.A. Horvathy, Conformal Carroll groups, J. Phys. A 47 (2014) 335204 [arXiv:1403.4213] [INSPIRE].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
A. Kapustin and M.J. Strassler, On mirror symmetry in three-dimensional Abelian gauge theories, JHEP 04 (1999) 021 [hep-th/9902033] [INSPIRE].
E. Witten, SL(2, Z) action on three-dimensional conformal field theories with Abelian symmetry, hep-th/0307041 [INSPIRE].
R.K. Mishra, A. Mohd and R. Sundrum, in preparation.
Z. Bern, S. Davies and J. Nohle, On loop corrections to subleading soft behavior of gluons and gravitons, Phys. Rev. D 90 (2014) 085015 [arXiv:1405.1015] [INSPIRE].
S. He, Y.-T. Huang and C. Wen, Loop corrections to soft theorems in gauge theories and gravity, JHEP 12 (2014) 115 [arXiv:1405.1410] [INSPIRE].
F. Cachazo and E.Y. Yuan, Are soft theorems renormalized?, arXiv:1405.3413 [INSPIRE].
Z. Bern, S. Davies, P. Di Vecchia and J. Nohle, Low-energy behavior of gluons and gravitons from gauge invariance, Phys. Rev. D 90 (2014) 084035 [arXiv:1406.6987] [INSPIRE].
T. He, D. Kapec, A.-M. Raclariu and A. Strominger, Loop-corrected Virasoro symmetry of 4D quantum gravity, JHEP 08 (2017) 050 [arXiv:1701.00496] [INSPIRE].
Y. Hamada, M.-S. Seo and G. Shiu, Memory in de Sitter space and Bondi-Metzner-Sachs-like supertranslations, Phys. Rev. D 96 (2017) 023509 [arXiv:1702.06928] [INSPIRE].
S. Deser and R.I. Nepomechie, Anomalous propagation of gauge fields in conformally flat spaces, Phys. Lett. B 132 (1983) 321 [INSPIRE].
S. Deser and R.I. Nepomechie, Gauge invariance versus masslessness in de Sitter space, Annals Phys. 154 (1984) 396 [INSPIRE].
S.J. Haco, S.W. Hawking, M.J. Perry and J.L. Bourjaily, The conformal BMS group, JHEP 11 (2017) 012 [arXiv:1701.08110] [INSPIRE].
S. Weinberg, Derivation of gauge invariance and the equivalence principle from Lorentz invariance of the S-matrix, Phys. Lett. 9 (1964) 357.
S. Weinberg, Photons and gravitons in S-matrix theory: derivation of charge conservation and equality of gravitational and inertial mass, Phys. Rev. 135 (1964) B1049 [INSPIRE].
S. Weinberg, Photons and gravitons in perturbation theory: derivation of Maxwell’s and Einstein’s equations, Phys. Rev. 138 (1965) B988 [INSPIRE].
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Mishra, R.K., Sundrum, R. Asymptotic symmetries, holography and topological hair. J. High Energ. Phys. 2018, 14 (2018). https://doi.org/10.1007/JHEP01(2018)014
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DOI: https://doi.org/10.1007/JHEP01(2018)014