Abstract
We investigate the supersymmetric versions of Bondi-Metzner-Sachs or, equivalently, conformal Carroll symmetry in boundary dimensions d > 3, with applications of flat space holography in mind. We identify the contraction of the relativistic symmetry relevant for our purposes and construct a finite-dimensional Carrollian superconformal algebra (CSA) before proposing an infinite-dimensional lift. We provide the superspace formulation for \( \mathcal{N} \) = 1 CSA and work towards an understanding of the representation theory of the algebra. We conclude with some aspects of \( \mathcal{N} \) > 1 CSA.
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References
G. ’t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [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, S matrices from AdS space-time, hep-th/9901076 [INSPIRE].
L. Susskind, Holography in the flat space limit, AIP Conf. Proc. 493 (1999) 98 [hep-th/9901079] [INSPIRE].
S. B. Giddings, Flat space scattering and bulk locality in the AdS/CFT correspondence, Phys. Rev. D 61 (2000) 106008 [hep-th/9907129] [INSPIRE].
A. Bagchi and R. Fareghbal, BMS/GCA redux: towards flatspace holography from non-relativistic symmetries, JHEP 10 (2012) 092 [arXiv:1203.5795] [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, R. Basu, A. Kakkar and A. Mehra, Flat holography: aspects of the dual field theory, JHEP 12 (2016) 147 [arXiv:1609.06203] [INSPIRE].
A. Bagchi, A. Mehra and P. Nandi, Field theories with conformal Carrollian symmetry, JHEP 05 (2019) 108 [arXiv:1901.10147] [INSPIRE].
A. Bagchi, R. Basu, A. Mehra and P. Nandi, Field theories on null manifolds, JHEP 02 (2020) 141 [arXiv:1912.09388] [INSPIRE].
K. Banerjee, R. Basu, A. Mehra, A. Mohan and A. Sharma, Interacting conformal Carrollian theories: cues from electrodynamics, Phys. Rev. D 103 (2021) 105001 [arXiv:2008.02829] [INSPIRE].
L. Donnay and C. Marteau, Carrollian physics at the black hole horizon, Class. Quant. Grav. 36 (2019) 165002 [arXiv:1903.09654] [INSPIRE].
G. Compère and A. Fiorucci, Advanced lectures on general relativity, arXiv:1801.07064 [INSPIRE].
D. Harlow and J.-Q. Wu, Covariant phase space with boundaries, JHEP 10 (2020) 146 [arXiv:1906.08616] [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. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128 (1962) 2851 [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].
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].
M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90 (2014) 124028 [arXiv:1408.2228] [INSPIRE].
G. Compère, A. Fiorucci and R. Ruzziconi, Superboost transitions, refraction memory and super-Lorentz charge algebra, JHEP 11 (2018) 200 [Erratum ibid. 04 (2020) 172] [arXiv:1810.00377] [INSPIRE].
D. Grumiller, A. Pérez, M. M. Sheikh-Jabbari, R. Troncoso and C. Zwikel, Spacetime structure near generic horizons and soft hair, Phys. Rev. Lett. 124 (2020) 041601 [arXiv:1908.09833] [INSPIRE].
A. Campoleoni, D. Francia and C. Heissenberg, On asymptotic symmetries in higher dimensions for any spin, JHEP 12 (2020) 129 [arXiv:2011.04420] [INSPIRE].
D. Kapec, V. Lysov, S. Pasterski and A. Strominger, Higher-dimensional supertranslations and Weinberg’s soft graviton theorem, Ann. Math. Sci. Appl. 02 (2017) 69 [arXiv:1502.07644] [INSPIRE].
O. Fuentealba, M. Henneaux, J. Matulich and C. Troessaert, Bondi-Metzner-Sachs group in five spacetime dimensions, Phys. Rev. Lett. 128 (2022) 051103 [arXiv:2111.09664] [INSPIRE].
S. Hollands and A. Ishibashi, Asymptotic flatness and Bondi energy in higher dimensional gravity, J. Math. Phys. 46 (2005) 022503 [gr-qc/0304054] [INSPIRE].
K. Tanabe, N. Tanahashi and T. Shiromizu, On asymptotic structure at null infinity in five dimensions, J. Math. Phys. 51 (2010) 062502 [arXiv:0909.0426] [INSPIRE].
K. Tanabe, S. Kinoshita and T. Shiromizu, Asymptotic flatness at null infinity in arbitrary dimensions, Phys. Rev. D 84 (2011) 044055 [arXiv:1104.0303] [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [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].
A. Bagchi, S. Detournay and D. Grumiller, Flat-space chiral gravity, Phys. Rev. Lett. 109 (2012) 151301 [arXiv:1208.1658] [INSPIRE].
A. Bagchi, S. Detournay, R. Fareghbal and J. Simón, Holography of 3D flat cosmological horizons, Phys. Rev. Lett. 110 (2013) 141302 [arXiv:1208.4372] [INSPIRE].
G. Barnich, Entropy of three-dimensional asymptotically flat cosmological solutions, JHEP 10 (2012) 095 [arXiv:1208.4371] [INSPIRE].
A. Bagchi, D. Grumiller and W. Merbis, Stress tensor correlators in three-dimensional gravity, Phys. Rev. D 93 (2016) 061502 [arXiv:1507.05620] [INSPIRE].
A. Bagchi, R. Basu, D. Grumiller and M. Riegler, Entanglement entropy in Galilean conformal field theories and flat holography, Phys. Rev. Lett. 114 (2015) 111602 [arXiv:1410.4089] [INSPIRE].
H. Jiang, W. Song and Q. Wen, Entanglement entropy in flat holography, JHEP 07 (2017) 142 [arXiv:1706.07552] [INSPIRE].
E. Hijano and C. Rabideau, Holographic entanglement and Poincaré blocks in three-dimensional flat space, JHEP 05 (2018) 068 [arXiv:1712.07131] [INSPIRE].
G. Barnich, A. Gomberoff and H. A. González, Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory, Phys. Rev. D 87 (2013) 124032 [arXiv:1210.0731] [INSPIRE].
A. Bagchi and R. Basu, 3D flat holography: entropy and logarithmic corrections, JHEP 03 (2014) 020 [arXiv:1312.5748] [INSPIRE].
A. Bagchi, S. Detournay, D. Grumiller and J. Simon, Cosmic evolution from phase transition of three-dimensional flat space, Phys. Rev. Lett. 111 (2013) 181301 [arXiv:1305.2919] [INSPIRE].
G. Barnich and B. Oblak, Notes on the BMS group in three dimensions. Part I. Induced representations, JHEP 06 (2014) 129 [arXiv:1403.5803] [INSPIRE].
C. Krishnan, A. Raju and S. Roy, A Grassmann path from AdS3 to flat space, JHEP 03 (2014) 036 [arXiv:1312.2941] [INSPIRE].
J. Hartong, Holographic reconstruction of 3D flat space-time, JHEP 10 (2016) 104 [arXiv:1511.01387] [INSPIRE].
A. Campoleoni, H. A. Gonzalez, B. Oblak and M. Riegler, BMS modules in three dimensions, Int. J. Mod. Phys. A 31 (2016) 1650068 [arXiv:1603.03812] [INSPIRE].
A. Bagchi, M. Gary and Zodinmawia, Bondi-Metzner-Sachs bootstrap, Phys. Rev. D 96 (2017) 025007 [arXiv:1612.01730] [INSPIRE].
E. Hijano, Semi-classical BMS3 blocks and flat holography, JHEP 10 (2018) 044 [arXiv:1805.00949] [INSPIRE].
A. Campoleoni and S. Pekar, Carrollian and Galilean conformal higher-spin algebras in any dimensions, JHEP 02 (2022) 150 [arXiv:2110.07794] [INSPIRE].
B. Chen, R. Liu and Y.-F. Zheng, On higher-dimensional Carrollian and Galilean conformal field theories, arXiv:2112.10514 [INSPIRE].
A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448 [INSPIRE].
S. Pasterski, Lectures on celestial amplitudes, Eur. Phys. J. C 81 (2021) 1062 [arXiv:2108.04801] [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].
G. Compère, A. Fiorucci and R. Ruzziconi, The Λ-BMS4 group of dS4 and new boundary conditions for AdS4, Class. Quant. Grav. 36 (2019) 195017 [Erratum ibid. 38 (2021) 229501] [arXiv:1905.00971] [INSPIRE].
J. A. Valiente-Kroon, A new class of obstructions to the smoothness of null infinity, Commun. Math. Phys. 244 (2004) 133 [gr-qc/0211024] [INSPIRE].
S. Hollands and R. M. Wald, Conformal null infinity does not exist for radiating solutions in odd spacetime dimensions, Class. Quant. Grav. 21 (2004) 5139 [gr-qc/0407014] [INSPIRE].
C. Duval, G. W. Gibbons and P. A. Horvathy, Conformal Carroll groups, J. Phys. A 47 (2014) 335204 [arXiv:1403.4213] [INSPIRE].
J. Levy-Leblond, Une nouvelle limite non-relativiste du group de Poincaré (in French), Ann. Inst. H. Poincaré 3 (1965) 1.
R. Basu and U. N. Chowdhury, Dynamical structure of Carrollian electrodynamics, JHEP 04 (2018) 111 [arXiv:1802.09366] [INSPIRE].
G. Barnich, L. Donnay, J. Matulich and R. Troncoso, Asymptotic symmetries and dynamics of three-dimensional flat supergravity, JHEP 08 (2014) 071 [arXiv:1407.4275] [INSPIRE].
N. Banerjee, D. P. Jatkar, I. Lodato, S. Mukhi and T. Neogi, Extended supersymmetric BMS3 algebras and their free field realisations, JHEP 11 (2016) 059 [arXiv:1609.09210] [INSPIRE].
I. Lodato and W. Merbis, Super-BMS3 algebras from N = 2 flat supergravities, JHEP 11 (2016) 150 [arXiv:1610.07506] [INSPIRE].
A. Bagchi, S. Chakrabortty and P. Parekh, Tensionless superstrings: view from the worldsheet, JHEP 10 (2016) 113 [arXiv:1606.09628] [INSPIRE].
R. Caroca, P. Concha, O. Fierro and E. Rodríguez, Three-dimensional Poincaré supergravity and N -extended supersymmetric BMS3 algebra, Phys. Lett. B 792 (2019) 93 [arXiv:1812.05065] [INSPIRE].
O. Fuentealba, J. Matulich and R. Troncoso, Asymptotic structure of N = 2 supergravity in 3D: extended super-BMS3 and nonlinear energy bounds, JHEP 09 (2017) 030 [arXiv:1706.07542] [INSPIRE].
A. Fotopoulos, S. Stieberger, T. R. Taylor and B. Zhu, Extended super BMS algebra of celestial CFT, JHEP 09 (2020) 198 [arXiv:2007.03785] [INSPIRE].
A. Bagchi, S. Chakrabortty and P. Parekh, Tensionless strings from worldsheet symmetries, JHEP 01 (2016) 158 [arXiv:1507.04361] [INSPIRE].
A. Bagchi, A. Banerjee, S. Chakrabortty and P. Parekh, Inhomogeneous tensionless superstrings, JHEP 02 (2018) 065 [arXiv:1710.03482] [INSPIRE].
A. Bagchi, A. Banerjee, S. Chakrabortty and P. Parekh, Exotic origins of tensionless superstrings, Phys. Lett. B 801 (2020) 135139 [arXiv:1811.10877] [INSPIRE].
N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
N. Banerjee, A. Mitra, D. Mukherjee and H. R. Safari, Supersymmetrization of deformed BMS algebras, arXiv:2201.09853 [INSPIRE].
N. Banerjee, A. Bhattacharjee, I. Lodato and T. Neogi, Maximally N -extended super-BMS3 algebras and generalized 3D gravity solutions, JHEP 01 (2019) 115 [arXiv:1807.06768] [INSPIRE].
A. Fotopoulos, S. Stieberger, T. R. Taylor and B. Zhu, Extended BMS algebra of celestial CFT, JHEP 03 (2020) 130 [arXiv:1912.10973] [INSPIRE].
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Bagchi, A., Grumiller, D. & Nandi, P. Carrollian superconformal theories and super BMS. J. High Energ. Phys. 2022, 44 (2022). https://doi.org/10.1007/JHEP05(2022)044
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DOI: https://doi.org/10.1007/JHEP05(2022)044