Abstract
We revisit the standard construction of the celestial stress tensor as a shadow of the subleading conformally soft graviton. In its original formulation there is an obstruction to reproducing the expected \( \overline{TT} \) OPE in the double soft limit. We propose a modification to the definition which circumvents this obstruction and then extend this change of basis beyond the conformally soft and single helicity sectors. In the process we investigate how (non)-commutativity of double soft limits is tied to the decoupling of primary descendants, and how our choice of celestial basis determines which symmetries are manifest at the level of the OPE beyond the MHV sector.
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References
S. Pasterski, M. Pate and A.-M. Raclariu, Celestial Holography, in the proceedings of the 2022 Snowmass Summer Study, arXiv:2111.11392 [INSPIRE].
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, Princeton University Press (2018), 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].
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].
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].
D. Kapec and P. Mitra, A d-Dimensional Stress Tensor for Minkd+2 Gravity, JHEP 05 (2018) 186 [arXiv:1711.04371] [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].
A. Fotopoulos, S. Stieberger, T.R. Taylor and B. Zhu, Extended Super BMS Algebra of Celestial CFT, JHEP 09 (2020) 198 [arXiv:2007.03785] [INSPIRE].
D. Kapec and P. Mitra, Shadows and soft exchange in celestial CFT, Phys. Rev. D 105 (2022) 026009 [arXiv:2109.00073] [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].
A. Guevara, Notes on Conformal Soft Theorems and Recursion Relations in Gravity, arXiv:1906.07810 [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, JHEP 09 (2020) 130 [arXiv:1905.09799] [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, S. Ghosh and S.S. Samal, Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes, JHEP 08 (2021) 067 [arXiv:2104.02546] [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+∞ Algebra and the Celestial Sphere: Infinite Towers of Soft Graviton, Photon, and Gluon Symmetries, Phys. Rev. Lett. 127 (2021) 221601 [INSPIRE].
L. Donnay, S. Pasterski and A. Puhm, Goldilocks modes and the three scattering bases, JHEP 06 (2022) 124 [arXiv:2202.11127] [INSPIRE].
N. Arkani-Hamed, M. Pate, A.-M. Raclariu and A. Strominger, Celestial amplitudes from UV to IR, JHEP 08 (2021) 062 [arXiv:2012.04208] [INSPIRE].
C.-M. Chang, Y.-T. Huang, Z.-X. Huang and W. Li, Bulk locality from the celestial amplitude, SciPost Phys. 12 (2022) 176 [arXiv:2106.11948] [INSPIRE].
J. Distler, R. Flauger and B. Horn, Double-soft graviton amplitudes and the extended BMS charge algebra, JHEP 08 (2019) 021 [arXiv:1808.09965] [INSPIRE].
A.H. Anupam, A. Kundu and K. Ray, Double soft graviton theorems and Bondi-Metzner-Sachs symmetries, Phys. Rev. D 97 (2018) 106019 [arXiv:1803.03023] [INSPIRE].
M. Campiglia and A. Laddha, BMS Algebra, Double Soft Theorems, and All That, arXiv:2106.14717 [INSPIRE].
D. Kapec, Soft Particles and Infinite-Dimensional Geometry, arXiv:2210.00606 [INSPIRE].
S. Banerjee, P. Pandey and P. Paul, Conformal properties of soft operators: Use of null states, Phys. Rev. D 101 (2020) 106014 [arXiv:1902.02309] [INSPIRE].
S. Banerjee and P. Pandey, Conformal properties of soft-operators. Part II. Use of null-states, JHEP 02 (2020) 067 [arXiv:1906.01650] [INSPIRE].
S. Pasterski, A. Puhm and E. Trevisani, Celestial diamonds: conformal multiplets in celestial CFT, JHEP 11 (2021) 072 [arXiv:2105.03516] [INSPIRE].
S. Pasterski, A. Puhm and E. Trevisani, Revisiting the conformally soft sector with celestial diamonds, JHEP 11 (2021) 143 [arXiv:2105.09792] [INSPIRE].
D. Simmons-Duffin, Projectors, Shadows, and Conformal Blocks, JHEP 04 (2014) 146 [arXiv:1204.3894] [INSPIRE].
F.M. Haehl, W. Reeves and M. Rozali, Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs, JHEP 11 (2019) 102 [arXiv:1909.05847] [INSPIRE].
A.E. Lipstein, Soft Theorems from Conformal Field Theory, JHEP 06 (2015) 166 [arXiv:1504.01364] [INSPIRE].
T. Klose et al., Double-Soft Limits of Gluons and Gravitons, JHEP 07 (2015) 135 [arXiv:1504.05558] [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].
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 and R. Ruzziconi, Coadjoint representation of the BMS group on celestial Riemann surfaces, JHEP 06 (2021) 079 [arXiv:2103.11253] [INSPIRE].
L. Donnay and R. Ruzziconi, BMS flux algebra in celestial holography, JHEP 11 (2021) 040 [arXiv:2108.11969] [INSPIRE].
S. Pasterski, A comment on loop corrections to the celestial stress tensor, JHEP 01 (2023) 025 [arXiv:2205.10901] [INSPIRE].
L. Donnay, K. Nguyen and R. Ruzziconi, Loop-corrected subleading soft theorem and the celestial stress tensor, JHEP 09 (2022) 063 [arXiv:2205.11477] [INSPIRE].
S. Pasterski, A. Strominger and A. Zhiboedov, New Gravitational Memories, JHEP 12 (2016) 053 [arXiv:1502.06120] [INSPIRE].
E. Himwich, Z. Mirzaiyan and S. Pasterski, A Note on the Subleading Soft Graviton, JHEP 04 (2021) 172 [arXiv:1902.01840] [INSPIRE].
A. Ball et al., Uplifting AdS3/CFT2 to flat space holography, JHEP 08 (2019) 168 [arXiv:1905.09809] [INSPIRE].
Y. Hu and S. Pasterski, Celestial conformal colliders, JHEP 02 (2023) 243 [arXiv:2211.14287] [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].
A. Sharma, Ambidextrous light transforms for celestial amplitudes, JHEP 01 (2022) 031 [arXiv:2107.06250] [INSPIRE].
A. Guevara, Celestial OPE blocks, arXiv:2108.12706 [INSPIRE].
H. Osborn, Conformal Blocks for Arbitrary Spins in Two Dimensions, Phys. Lett. B 718 (2012) 169 [arXiv:1205.1941] [INSPIRE].
I.M. Gel’fand and G.E. Shilov, Generalized Functions, Volume 1: Properties and Operations, Academic Press (1964).
J.H. Schwarz, Diffeomorphism Symmetry in Two Dimensions and Celestial Holography, arXiv:2208.13304 [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].
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].
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].
S. Banerjee and S. Ghosh, MHV gluon scattering amplitudes from celestial current algebras, JHEP 10 (2021) 111 [arXiv:2011.00017] [INSPIRE].
I.M. Gel’fand, M.I. Graev and N.Y. Vilenkin, Generalized Functions, Volume 5: Integral Geometry and Representation Theory, AMS Chelsea Publishing (1966).
S. Pasterski and H. Verlinde, HPS meets AMPS: how soft hair dissolves the firewall, JHEP 09 (2021) 099 [arXiv:2012.03850] [INSPIRE].
S. He, P. Mao and X.-C. Mao, \( T\overline{T} \) deformed soft theorem, arXiv:2209.01953 [INSPIRE].
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Banerjee, S., Pasterski, S. Revisiting the shadow stress tensor in celestial CFT. J. High Energ. Phys. 2023, 118 (2023). https://doi.org/10.1007/JHEP04(2023)118
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DOI: https://doi.org/10.1007/JHEP04(2023)118