Abstract
We study two-dimensional celestial conformal field theory describing four- dimensional \( \mathcal{N} \) =1 supergravity/Yang-Mills systems and show that the underlying symmetry is a supersymmetric generalization of BMS symmetry. We construct fermionic conformal primary wave functions and show how they are related via supersymmetry to their bosonic partners. We use soft and collinear theorems of supersymmetric Einstein-Yang- Mills theory to derive the OPEs of the operators associated to massless particles. The bosonic and fermionic soft theorems are shown to form a sequence under supersymmetric Ward identities. In analogy with the energy momentum tensor, the supercurrents are shadow transforms of soft gravitino operators and generate an infinite-dimensional super- symmetry algebra. The algebra of \( {\mathfrak{sbms}}_4 \) generators agrees with the expectations based on earlier work on the asymptotic symmetry group of supergravity. We also show that the supertranslation operator can be written as a product of holomorphic and anti-holomorphic supercurrents.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].
F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [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].
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96 (2017) 065022 [arXiv:1705.01027] [INSPIRE].
S. Pasterski, S.-H. Shao and A. Strominger, Gluon Amplitudes as 2d Conformal Correlators, Phys. Rev. D 96 (2017) 085006 [arXiv:1706.03917] [INSPIRE].
L. Donnay, A. Puhm and A. Strominger, Conformally Soft Photons and Gravitons, JHEP 01 (2019) 184 [arXiv:1810.05219] [INSPIRE].
W. Fan, A. Fotopoulos and T.R. Taylor, Soft Limits of Yang-Mills Amplitudes and Conformal Correlators, JHEP 05 (2019) 121 [arXiv:1903.01676] [INSPIRE].
M. Pate, A.-M. Raclariu and A. Strominger, Conformally Soft Theorem in Gauge Theory, Phys. Rev. D 100 (2019) 085017 [arXiv:1904.10831] [INSPIRE].
D. Nandan, A. Schreiber, A. Volovich and M. Zlotnikov, Celestial Amplitudes: Conformal Partial Waves and Soft Limits, JHEP 10 (2019) 018 [arXiv:1904.10940] [INSPIRE].
T. Adamo, L. Mason and A. Sharma, Celestial amplitudes and conformal soft theorems, Class. Quant. Grav. 36 (2019) 205018 [arXiv:1905.09224] [INSPIRE].
A. Puhm, Conformally Soft Theorem in Gravity, arXiv:1905.09799 [INSPIRE].
A. Guevara, Notes on Conformal Soft Theorems and Recursion Relations in Gravity, arXiv:1906.07810 [INSPIRE].
A. Fotopoulos and T.R. Taylor, Primary Fields in Celestial CFT, JHEP 10 (2019) 167 [arXiv:1906.10149] [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].
M.A. Awada, G.W. Gibbons and W.T. Shaw, Conformal supergravity, twistors and the super BMS group, Annals Phys. 171 (1986) 52 [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].
G. Barnich, Entropy of three-dimensional asymptotically flat cosmological solutions, JHEP 10 (2012) 095 [arXiv:1208.4371] [INSPIRE].
A. Bagchi, S. Detournay, R. Fareghbal and J. Sim´on, Holography of 3D Flat Cosmological Horizons, Phys. Rev. Lett. 110 (2013) 141302 [arXiv:1208.4372] [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].
I. Lodato and W. Merbis, Super-BMS3 algebras from \( \mathcal{N} \) = 2 flat supergravities, JHEP 11 (2016) 150 [arXiv:1610.07506] [INSPIRE].
O. Fuentealba, J. Matulich and R. Troncoso, Asymptotic structure of \( \mathcal{N} \) = 2 supergravity in 3D: extended super-BMS3 and nonlinear energy bounds, JHEP 09 (2017) 030 [arXiv:1706.07542] [INSPIRE].
T.T. Dumitrescu, T. He, P. Mitra and A. Strominger, Infinite-Dimensional Fermionic Symmetry in Supersymmetric Gauge Theories, arXiv:1511.07429 [INSPIRE].
V. Lysov, Asymptotic Fermionic Symmetry From Soft Gravitino Theorem, arXiv:1512.03015 [INSPIRE].
S.G. Avery and B.U.W. Schwab, Residual Local Supersymmetry and the Soft Gravitino, Phys. Rev. Lett. 116 (2016) 171601 [arXiv:1512.02657] [INSPIRE].
M.T. Grisaru, H.N. Pendleton and P. van Nieuwenhuizen, Supergravity and the S Matrix, Phys. Rev. D 15 (1977) 996 [INSPIRE].
M.T. Grisaru and H.N. Pendleton, Some Properties of Scattering Amplitudes in Supersymmetric Theories, Nucl. Phys. B 124 (1977) 81 [INSPIRE].
S.J. Parke and T.R. Taylor, Perturbative QCD Utilizing Extended Supersymmetry, Phys. Lett. B 157 (1985) 81 [Erratum ibid. 174 (1986) 465] [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].
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].
G. Barnich, Centrally extended BMS4 Lie algebroid, JHEP 06 (2017) 007 [arXiv:1703.08704] [INSPIRE].
W. Fan, A. Fotopoulos, S. Stieberger and T.R. Taylor, On Sugawara construction on Celestial Sphere, arXiv:2005.10666 [INSPIRE].
T.R. Taylor, A Course in Amplitudes, Phys. Rept. 691 (2017) 1 [arXiv:1703.05670] [INSPIRE].
M. Pate, A.-M. Raclariu, A. Strominger and E.Y. Yuan, Celestial Operator Products of Gluons and Gravitons, arXiv:1910.07424 [INSPIRE].
S. Stieberger and T.R. Taylor, Strings on Celestial Sphere, Nucl. Phys. B 935 (2018) 388 [arXiv:1806.05688] [INSPIRE].
L. Donnay, S. Pasterski and A. Puhm, Asymptotic Symmetries and Celestial CFT, arXiv:2005.08990 [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].
N.E.J. Bjerrum-Bohr and O.T. Engelund, Gravitino Interactions from Yang-Mills Theory, Phys. Rev. D 81 (2010) 105009 [arXiv:1002.2279] [INSPIRE].
S. Stieberger and T.R. Taylor, Subleading terms in the collinear limit of Yang-Mills amplitudes, Phys. Lett. B 750 (2015) 587 [arXiv:1508.01116] [INSPIRE].
E. Casali, Soft sub-leading divergences in Yang-Mills amplitudes, JHEP 08 (2014) 077 [arXiv:1404.5551] [INSPIRE].
S. Stieberger and T.R. Taylor, Symmetries of Celestial Amplitudes, Phys. Lett. B 793 (2019) 141 [arXiv:1812.01080] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2007.03785
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
Fotopoulos, A., Stieberger, S., Taylor, T.R. et al. Extended super BMS algebra of celestial CFT. J. High Energ. Phys. 2020, 198 (2020). https://doi.org/10.1007/JHEP09(2020)198
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2020)198