Abstract
Symmetry algebras deriving from towers of soft theorems can be deformed by a short list of higher-dimension Wilsonian corrections to the effective action. We study the simplest of these deformations in gauge theory arising from a massless complex scalar coupled to F2. The soft gauge symmetry ‘s-algebra’, compactly realized as a higher-spin current algebra acting on the celestial sphere, is deformed and enlarged to an associative algebra containing soft scalar generators. This deformed soft algebra is found to be non-abelian even in abelian gauge theory. A two-parameter family of central extensions of the s-subalgebra are generated by shifting and decoupling the scalar generators. It is shown that these central extensions can also be generated by expanding around a certain non-trivial but Lorentz invariant shockwave type background for the scalar field.
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References
A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448 [INSPIRE].
A. Strominger, w1+∞ algebra and the celestial sphere: infinite towers of soft graviton, photon, and gluon symmetries, Phys. Rev. Lett. 127 (2021) 221601 [INSPIRE].
A. Guevara, E. Himwich, M. Pate and A. Strominger, Holographic symmetry algebras for gauge theory and gravity, JHEP 11 (2021) 152 [arXiv:2103.03961] [INSPIRE].
A. Ball, S.A. Narayanan, J. Salzer and A. Strominger, Perturbatively exact w1+∞ asymptotic symmetry of quantum self-dual gravity, JHEP 01 (2022) 114 [arXiv:2111.10392] [INSPIRE].
L. Ren, M. Spradlin, A. Yelleshpur Srikant and A. Volovich, On effective field theories with celestial duals, JHEP 08 (2022) 251 [arXiv:2206.08322] [INSPIRE].
K. Costello and N.M. Paquette, Celestial holography meets twisted holography: 4d amplitudes from chiral correlators, JHEP 10 (2022) 193 [arXiv:2201.02595] [INSPIRE].
K. Costello and N.M. Paquette, Associativity of one-loop corrections to the celestial operator product expansion, Phys. Rev. Lett. 129 (2022) 231604 [arXiv:2204.05301] [INSPIRE].
R. Bittleston, On the associativity of 1-loop corrections to the celestial operator product in gravity, JHEP 01 (2023) 018 [arXiv:2211.06417] [INSPIRE].
A. Ball, Celestial locality and the Jacobi identity, JHEP 01 (2023) 146 [arXiv:2211.09151] [INSPIRE].
H. Elvang, C.R.T. Jones and S.G. Naculich, Soft photon and graviton theorems in effective field theory, Phys. Rev. Lett. 118 (2017) 231601 [arXiv:1611.07534] [INSPIRE].
M. Pate, A.-M. Raclariu, A. Strominger and E.Y. Yuan, Celestial operator products of gluons and gravitons, Rev. Math. Phys. 33 (2021) 2140003 [arXiv:1910.07424] [INSPIRE].
L.J. Dixon, E.W.N. Glover and V.V. Khoze, MHV rules for Higgs plus multi-gluon amplitudes, JHEP 12 (2004) 015 [hep-th/0411092] [INSPIRE].
G. Carosi et al., Probing the axion-photon coupling: phenomenological and experimental perspectives. A Snowmass white paper, in the proceedings of Community summer study 2013: Snowmass on the Mississippi, (2013) [arXiv:1309.7035] [INSPIRE].
D. Aristizabal Sierra, O.G. Miranda, D.K. Papoulias and G.S. Garcia, Neutrino magnetic and electric dipole moments: from measurements to parameter space, Phys. Rev. D 105 (2022) 035027 [arXiv:2112.12817] [INSPIRE].
W. Fan et al., Elements of celestial conformal field theory, JHEP 08 (2022) 213 [arXiv:2202.08288] [INSPIRE].
E. Casali, W. Melton and A. Strominger, Celestial amplitudes as AdS-Witten diagrams, JHEP 11 (2022) 140 [arXiv:2204.10249] [INSPIRE].
W. Fan et al., Celestial Yang-Mills amplitudes and D = 4 conformal blocks, JHEP 09 (2022) 182 [arXiv:2206.08979] [INSPIRE].
S. Stieberger, T.R. Taylor and B. Zhu, Celestial Liouville theory for Yang-Mills amplitudes, Phys. Lett. B 836 (2023) 137588 [arXiv:2209.02724] [INSPIRE].
R. Gonzo, T. McLoughlin and A. Puhm, Celestial holography on Kerr-Schild backgrounds, JHEP 10 (2022) 073 [arXiv:2207.13719] [INSPIRE].
D. Kapec, Y.T.A. Law and S.A. Narayanan, Soft scalars and the geometry of the space of celestial conformal field theories, Phys. Rev. D 107 (2023) 046024 [arXiv:2205.10935] [INSPIRE].
A. Atanasov et al., (2, 2) scattering and the celestial torus, JHEP 07 (2021) 083 [arXiv:2101.09591] [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].
E. Himwich, M. Pate and K. Singh, Celestial operator product expansions and w1+∞ symmetry for all spins, JHEP 01 (2022) 080 [arXiv:2108.07763] [INSPIRE].
A. Strominger, Asymptotic symmetries of Yang-Mills theory, JHEP 07 (2014) 151 [arXiv:1308.0589] [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].
J. Mago, L. Ren, A.Y. Srikant and A. Volovich, Deformed w1+∞ algebras in the celestial CFT, arXiv:2111.11356 [INSPIRE].
K. Costello, N.M. Paquette and A. Sharma, Top-down holography in an asymptotically flat spacetime, Phys. Rev. Lett. 130 (2023) 061602 [arXiv:2208.14233] [INSPIRE].
P. Di Francesco, P. Mathieu and D. Sénéchal, Conformal field theory, Springer-Verlag, New York, NY, U.S.A. (1997) [INSPIRE].
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Melton, W., Narayanan, S.A. & Strominger, A. Deforming soft algebras for gauge theory. J. High Energ. Phys. 2023, 233 (2023). https://doi.org/10.1007/JHEP03(2023)233
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DOI: https://doi.org/10.1007/JHEP03(2023)233