Abstract
In this paper we study the tree-level OPE between two positive helicity outgoing gluons in the celestial CFT for the Yang-Mills theory chirally coupled to a massive scalar background. This theory breaks the translation as well as scale invariance. We compute the subleading terms in the OPE expansion and show that they are same as the subleading terms of the OPE expansions in the MHV sector. As a result the amplitudes of this theory also satisfy the set of differential equations obtained previously for MHV amplitudes in pure YM theory. This is not surprising because the symmetries coming from the leading and subleading soft gluon theorems do not change in the presence of a massive scalar background.
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S. Pasterski, S.-H. Shao and A. Strominger, Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere, Phys. Rev. D 96 (2017) 065026 [arXiv:1701.00049] [INSPIRE].
S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96 (2017) 065022 [arXiv:1705.01027] [INSPIRE].
S. Banerjee, Null Infinity and Unitary Representation of The Poincare Group, JHEP 01 (2019) 205 [arXiv:1801.10171] [INSPIRE].
L. Freidel, D. Pranzetti and A.-M. Raclariu, A discrete basis for celestial holography, arXiv:2212.12469 [INSPIRE].
J. Cotler, N. Miller and A. Strominger, An integer basis for celestial amplitudes, JHEP 08 (2023) 192 [arXiv:2302.04905] [INSPIRE].
S. Banerjee, S. Ghosh and P. Paul, MHV graviton scattering amplitudes and current algebra on the celestial sphere, JHEP 02 (2021) 176 [arXiv:2008.04330] [INSPIRE].
S. Banerjee and S. Ghosh, MHV gluon scattering amplitudes from celestial current algebras, JHEP 10 (2021) 111 [arXiv:2011.00017] [INSPIRE].
S. Ebert, A. Sharma and D. Wang, Descendants in celestial CFT and emergent multi-collinear factorization, JHEP 03 (2021) 030 [arXiv:2009.07881] [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. Strominger, w1+∞ and the Celestial Sphere, arXiv:2105.14346 [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].
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].
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, D. Kapec, A.-M. Raclariu and A. Strominger, Loop-Corrected Virasoro Symmetry of 4D Quantum Gravity, JHEP 08 (2017) 050 [arXiv:1701.00496] [INSPIRE].
L. Donnay, S. Pasterski and A. Puhm, Asymptotic Symmetries and Celestial CFT, JHEP 09 (2020) 176 [arXiv:2005.08990] [INSPIRE].
S. Stieberger and T.R. Taylor, Symmetries of Celestial Amplitudes, Phys. Lett. B 793 (2019) 141 [arXiv:1812.01080] [INSPIRE].
S. Banerjee and S. Pasterski, Revisiting the shadow stress tensor in celestial CFT, JHEP 04 (2023) 118 [arXiv:2212.00257] [INSPIRE].
A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
A. Strominger, Asymptotic Symmetries of Yang-Mills Theory, JHEP 07 (2014) 151 [arXiv:1308.0589] [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].
L. Donnay, A. Puhm and A. Strominger, Conformally Soft Photons and Gravitons, JHEP 01 (2019) 184 [arXiv:1810.05219] [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].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New Symmetries of Massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [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, V. Lysov and A. Strominger, Asymptotic Symmetries of Massless QED in Even Dimensions, Adv. Theor. Math. Phys. 21 (2017) 1747 [arXiv:1412.2763] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries of QED and Weinberg’s soft photon theorem, JHEP 07 (2015) 115 [arXiv:1505.05346] [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].
T. He and P. Mitra, Covariant Phase Space and Soft Factorization in Non-Abelian Gauge Theories, JHEP 03 (2021) 015 [arXiv:2009.14334] [INSPIRE].
W. Fan et al., Elements of celestial conformal field theory, JHEP 08 (2022) 213 [arXiv:2202.08288] [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].
E. Casali, W. Melton and A. Strominger, Celestial amplitudes as AdS-Witten diagrams, JHEP 11 (2022) 140 [arXiv:2204.10249] [INSPIRE].
A. Atanasov et al., (2, 2) Scattering and the celestial torus, JHEP 07 (2021) 083 [arXiv:2101.09591] [INSPIRE].
A. Atanasov, W. Melton, A.-M. Raclariu and A. Strominger, Conformal block expansion in celestial CFT, Phys. Rev. D 104 (2021) 126033 [arXiv:2104.13432] [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].
S. Banerjee, S. Ghosh and R. Gonzo, BMS symmetry of celestial OPE, JHEP 04 (2020) 130 [arXiv:2002.00975] [INSPIRE].
S. Banerjee, S. Ghosh and P. Paul, (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes, JHEP 09 (2022) 236 [arXiv:2108.04262] [INSPIRE].
R. Bhardwaj et al., Loop-level gluon OPEs in celestial holography, JHEP 11 (2022) 171 [arXiv:2208.14416] [INSPIRE].
A.-M. Raclariu, Lectures on Celestial Holography, arXiv:2107.02075 [INSPIRE].
S. Pasterski, Lectures on celestial amplitudes, Eur. Phys. J. C 81 (2021) 1062 [arXiv:2108.04801] [INSPIRE].
S. Pasterski, M. Pate and A.-M. Raclariu, Celestial Holography, in the proceedings of the Snowmass 2021, Seattle U.S.A., July 17–26 (2022) [arXiv:2111.11392] [INSPIRE].
T. McLoughlin, A. Puhm and A.-M. Raclariu, The SAGEX review on scattering amplitudes chapter 11: soft theorems and celestial amplitudes, J. Phys. A 55 (2022) 443012 [arXiv:2203.13022] [INSPIRE].
S. Banerjee, S. Ghosh and S.S. Samal, Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes, JHEP 08 (2021) 067 [arXiv:2104.02546] [INSPIRE].
S. Banerjee, H. Kulkarni and P. Paul, An infinite family of w1+∞ invariant theories on the celestial sphere, JHEP 05 (2023) 063 [arXiv:2301.13225] [INSPIRE].
Y. Hu, L. Ren, A.Y. Srikant and A. Volovich, Celestial dual superconformal symmetry, MHV amplitudes and differential equations, JHEP 12 (2021) 171 [arXiv:2106.16111] [INSPIRE].
Y. Hu and S. Pasterski, Celestial recursion, JHEP 01 (2023) 151 [arXiv:2208.11635] [INSPIRE].
W. Melton, S.A. Narayanan and A. Strominger, Deforming soft algebras for gauge theory, JHEP 03 (2023) 233 [arXiv:2212.08643] [INSPIRE].
Acknowledgments
The work of SB is partially supported by the Swarnajayanti Fellowship (File No- SB/SJF/2021-22/14) of the Department of Science and Technology and SERB, India. PP would like to thank the organizers and the participants of the CHEP in-house symposium, 2022 held in IISc, Bangalore where part of this work was presented. The work of PP is supported by an IOE endowed postdoctoral position at IISc, Bangalore, India.
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Banerjee, S., Mandal, R., Manu, A. et al. MHV gluon scattering in the massive scalar background and celestial OPE. J. High Energ. Phys. 2023, 7 (2023). https://doi.org/10.1007/JHEP10(2023)007
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DOI: https://doi.org/10.1007/JHEP10(2023)007