Abstract
Scattering amplitudes of any four-dimensional theory with nonabelian gauge group \( \mathcal{G} \) may be recast as two-dimensional correlation functions on the asymptotic twosphere at null infinity. The soft gluon theorem is shown, for massless theories at the semiclassical level, to be the Ward identity of a holomorphic two-dimensional \( \mathcal{G} \)-Kac-Moody symmetry acting on these correlation functions. Holomorphic Kac-Moody current insertions are positive helicity soft gluon insertions. The Kac-Moody transformations are a CPT invariant subgroup of gauge transformations which act nontrivially at null infinity and comprise the four-dimensional asymptotic symmetry group.
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References
F.A. Berends and W.T. Giele, Multiple Soft Gluon Radiation in Parton Processes, Nucl. Phys. B 313 (1989) 595 [INSPIRE].
V.P. Nair, A Current Algebra for Some Gauge Theory Amplitudes, Phys. Lett. B 214 (1988) 215 [INSPIRE].
A. Strominger, Asymptotic Symmetries of Yang-Mills Theory, JHEP 07 (2014) 151 [arXiv:1308.0589] [INSPIRE].
H. Bondi, M. van der Burg and A. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
R. 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].
G. Barnich and C. Troessaert, Supertranslations call for superrotations, PoS(CNCFG2010)010 [arXiv:1102.4632] [INSPIRE].
G. Barnich and C. Troessaert, BMS charge algebra, JHEP 12 (2011) 105 [arXiv:1106.0213] [INSPIRE].
A. Ashtekar and M. Streubel, Symplectic Geometry of Radiative Modes and Conserved Quantities at Null Infinity, Proc. Roy. Soc. Lond. A 376 (1981) 585 [INSPIRE].
A. Ashtekar, Asymptotic Quantization of the Gravitational Field, Phys. Rev. Lett. 46 (1981) 573 [INSPIRE].
A. Ashtekar, Asymptotic Quantization: Based on 1984 Naples Lectures, Bibliopolis, Naples, Italy (1987) [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 \( \mathcal{S} \) -matrix, JHEP 08 (2014) 058 [arXiv:1406.3312] [INSPIRE].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New Symmetries of Massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [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].
D. Kapec, V. Lysov and A. Strominger, Asymptotic Symmetries of Massless QED in Even Dimensions, arXiv:1412.2763 [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles in Arbitrary Dimensions, Phys. Rev. Lett. 113 (2014) 171601 [arXiv:1307.2199] [INSPIRE].
F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].
E. Casali, Soft sub-leading divergences in Yang-Mills amplitudes, JHEP 08 (2014) 077 [arXiv:1404.5551] [INSPIRE].
B.U.W. Schwab and A. Volovich, Subleading Soft Theorem in Arbitrary Dimensions from Scattering Equations, Phys. Rev. Lett. 113 (2014) 101601 [arXiv:1404.7749] [INSPIRE].
A.J. Larkoski, Conformal Invariance of the Subleading Soft Theorem in Gauge Theory, Phys. Rev. D 90 (2014) 087701 [arXiv:1405.2346] [INSPIRE].
A.J. Larkoski, D. Neill and I.W. Stewart, Soft Theorems from Effective Field Theory, JHEP 06 (2015) 077 [arXiv:1412.3108] [INSPIRE].
N. Afkhami-Jeddi, Soft Graviton Theorem in Arbitrary Dimensions, arXiv:1405.3533 [INSPIRE].
T. Adamo, E. Casali and D. Skinner, Perturbative gravity at null infinity, Class. Quant. Grav. 31 (2014) 225008 [arXiv:1405.5122] [INSPIRE].
Y. Geyer, A.E. Lipstein and L. Mason, Ambitwistor strings at null infinity and (subleading) soft limits, Class. Quant. Grav. 32 (2015) 055003 [arXiv:1406.1462] [INSPIRE].
B.U.W. Schwab, Subleading Soft Factor for String Disk Amplitudes, JHEP 08 (2014) 062 [arXiv:1406.4172] [INSPIRE].
M. Bianchi, S. He, Y.-t. Huang and C. Wen, More on Soft Theorems: Trees, Loops and Strings, Phys. Rev. D 92 (2015) 065022 [arXiv:1406.5155] [INSPIRE].
A.P. Balachandran, S. Kürkçüoğlu, A.R. de Queiroz and S. Vaidya, Spontaneous Lorentz Violation: The Case of Infrared QED, Eur. Phys. J. C 75 (2015) 89 [arXiv:1406.5845] [INSPIRE].
J. Broedel, M. de Leeuw, J. Plefka and M. Rosso, Constraining subleading soft gluon and graviton theorems, Phys. Rev. D 90 (2014) 065024 [arXiv:1406.6574] [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].
A. Campoleoni and M. Henneaux, Asymptotic symmetries of three-dimensional higher-spin gravity: the metric approach, JHEP 03 (2015) 143 [arXiv:1412.6774] [INSPIRE].
A. Mohd, A note on asymptotic symmetries and soft-photon theorem, JHEP 02 (2015) 060 [arXiv:1412.5365] [INSPIRE].
P.-H. Lambert, Conformal symmetries of gravity from asymptotic methods: further developments, arXiv:1409.4693 [INSPIRE].
M. Campiglia and A. Laddha, New symmetries for the Gravitational S-matrix, JHEP 04 (2015) 076 [arXiv:1502.02318] [INSPIRE].
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].
S. Caron-Huot, private communication, (2014).
J. Maldacena, private communication, (2014).
I. Feige and M.D. Schwartz, Hard-Soft-Collinear Factorization to All Orders, Phys. Rev. D 90 (2014) 105020 [arXiv:1403.6472] [INSPIRE].
T. Banks, A critique of pure string theory: Heterodox opinions of diverse dimensions, hep-th/0306074 [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].
F. Cachazo and E.Y. Yuan, Are Soft Theorems Renormalized?, arXiv:1405.3413 [INSPIRE].
J. Maldacena and A. Zhiboedov, Notes on Soft Factors, unpublished (2012) and private communication.
H. Elvang and Y.-t. Huang, Scattering Amplitudes, arXiv:1308.1697 [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].
M.D. Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press, (2014), ISBN-9781107034730.
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He, T., Mitra, P. & Strominger, A. 2D Kac-Moody symmetry of 4D Yang-Mills theory. J. High Energ. Phys. 2016, 137 (2016). https://doi.org/10.1007/JHEP10(2016)137
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DOI: https://doi.org/10.1007/JHEP10(2016)137