Abstract
The gravitational \( \mathcal{S} \)-matrix defined with an infrared (IR) cutoff factorizes into hard and soft factors. The soft factor is universal and contains all the IR and collinear divergences. Here we show, in a momentum space basis, that the intricate expression for the soft factor is fully reproduced by two boundary currents, which live on the celestial sphere. The first of these is the supertranslation current, which generates spacetime supertranslations. The second is its symplectic partner, the Goldstone current for spontaneously broken supertranslations. The current algebra has an off-diagonal level structure involving the gravitational cusp anomalous dimension and the logarithm of the IR cutoff. It is further shown that the gravitational memory effect is contained as an IR safe observable within the soft \( \mathcal{S} \)-matrix.
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References
F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].
D. Kapec, V. Lysov, S. Pasterski and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity \( \mathcal{S} \)-matrix, JHEP 08 (2014) 058 [arXiv:1406.3312] [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].
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [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].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New Symmetries of Massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries of QED and Weinberg’s soft photon theorem, JHEP 07 (2015) 115 [arXiv:1505.05346] [INSPIRE].
D. Kapec, M. Pate and A. Strominger, New Symmetries of QED, Adv. Theor. Math. Phys. 21 (2017) 1769 [arXiv:1506.02906] [INSPIRE].
D. Kapec, M. Perry, A.-M. Raclariu and A. Strominger, Infrared Divergences in QED, Revisited, Phys. Rev. D 96 (2017) 085002 [arXiv:1705.04311] [INSPIRE].
S. Choi, U. Kol and R. Akhoury, Asymptotic Dynamics in Perturbative Quantum Gravity and BMS Supertranslations, JHEP 01 (2018) 142 [arXiv:1708.05717] [INSPIRE].
S. Choi and R. Akhoury, BMS Supertranslation Symmetry Implies Faddeev-Kulish Amplitudes, JHEP 02 (2018) 171 [arXiv:1712.04551] [INSPIRE].
A. Nande, M. Pate and A. Strominger, Soft Factorization in QED from 2D Kac-Moody Symmetry, JHEP 02 (2018) 079 [arXiv:1705.00608] [INSPIRE].
S. Choi, S. Sandeep Pradhan and R. Akhoury, Supertranslation Hair of Schwarzschild Black Hole: A Wilson Line Perspective, JHEP 01 (2020) 013 [arXiv:1910.05882] [INSPIRE].
C.D. White, Factorization Properties of Soft Graviton Amplitudes, JHEP 05 (2011) 060 [arXiv:1103.2981] [INSPIRE].
D.J. Miller and C.D. White, The Gravitational cusp anomalous dimension from AdS space, Phys. Rev. D 85 (2012) 104034 [arXiv:1201.2358] [INSPIRE].
A. Strominger and A. Zhiboedov, Gravitational Memory, BMS Supertranslations and Soft Theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
N. Arkani-Hamed, M. Pate, A.-M. Raclariu and A. Strominger, Celestial Amplitudes from UV to IR, to appear.
L. Donnay, A. Puhm and A. Strominger, Conformally Soft Photons and Gravitons, JHEP 01 (2019) 184 [arXiv:1810.05219] [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].
S.G. Naculich and H.J. Schnitzer, Eikonal methods applied to gravitational scattering amplitudes, JHEP 05 (2011) 087 [arXiv:1101.1524] [INSPIRE].
V.B. Braginsky and K.S. Thorne, Gravitational-wave bursts with memory and experimental prospects, Nature 327 (1987) 123.
M. Campiglia, Null to time-like infinity Green’s functions for asymptotic symmetries in Minkowski spacetime, JHEP 11 (2015) 160 [arXiv:1509.01408] [INSPIRE].
S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations, Cambridge University Press (2005) [INSPIRE].
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ArXiv ePrint: 2005.13433
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Himwich, E., Narayanan, S., Pate, M. et al. The soft \( \mathcal{S} \)-matrix in gravity. J. High Energ. Phys. 2020, 129 (2020). https://doi.org/10.1007/JHEP09(2020)129
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DOI: https://doi.org/10.1007/JHEP09(2020)129