Abstract
Celestial diamonds encode the structure of global conformal multiplets in 2D celestial CFT and offer a natural language for describing the conformally soft sector. The operators appearing at their left and right corners give rise to conformally soft factorization theorems, the bottom corners correspond to conserved charges, and the top corners to conformal dressings. We show that conformally soft charges can be expressed in terms of light ray integrals that select modes of the appropriate conformal weights. They reside at the bottom corners of memory diamonds, and ascend to generalized currents. We then identify the top corners of the associated Goldstone diamonds with conformal Faddeev-Kulish dressings and compute the sub-leading conformally soft dressings in gauge theory and gravity which are important for finding nontrivial central extensions. Finally, we combine these ingredients to speculate on 2D effective descriptions for the conformally soft sector of celestial CFT.
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S. Pasterski, S.-H. Shao and A. Strominger, Gluon amplitudes as 2d conformal correlators, Phys. Rev. D 96 (2017) 085006 [arXiv:1706.03917] [INSPIRE].
L. Donnay, A. Puhm and A. Strominger, Conformally soft photons and gravitons, JHEP 01 (2019) 184 [arXiv:1810.05219] [INSPIRE].
S. Pasterski and A. Puhm, Shifting spin on the celestial sphere, Phys. Rev. D 104 (2021) 086020 [arXiv:2012.15694] [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].
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].
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].
K. Nguyen and J. Salzer, The effective action of superrotation modes, JHEP 02 (2021) 108 [arXiv:2008.03321] [INSPIRE].
K. Nguyen, Reparametrization modes in 2d CFT and the effective theory of stress tensor exchanges, JHEP 05 (2021) 029 [arXiv:2101.08800] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90 (2014) 124028 [arXiv:1408.2228] [INSPIRE].
G. Compère, A. Fiorucci and R. Ruzziconi, Superboost transitions, refraction memory and super-Lorentz charge algebra, JHEP 11 (2018) 200 [Erratum ibid. 04 (2020) 172] [arXiv:1810.00377] [INSPIRE].
L. Donnay, S. Pasterski and A. Puhm, Asymptotic symmetries and celestial CFT, JHEP 09 (2020) 176 [arXiv:2005.08990] [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].
M. Pate, A.-M. Raclariu and A. Strominger, Conformally soft theorem in gauge theory, Phys. Rev. D 100 (2019) 085017 [arXiv:1904.10831] [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].
A. Guevara, Notes on conformal soft theorems and recursion relations in gravity, arXiv:1906.07810 [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].
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].
S. Pasterski, A. Puhm and E. Trevisani, Celestial diamonds: conformal multiplets in celestial CFT, arXiv:2105.03516 [INSPIRE].
S. Banerjee, Null infinity and unitary representation of the Poincaré group, JHEP 01 (2019) 205 [arXiv:1801.10171] [INSPIRE].
S. Banerjee, Symmetries of free massless particles and soft theorems, Gen. Rel. Grav. 51 (2019) 128 [arXiv:1804.06646] [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].
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].
A. Strominger, On BMS invariance of gravitational scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
S. Choi and R. Akhoury, Subleading soft dressings of asymptotic states in QED and perturbative quantum gravity, JHEP 09 (2019) 031 [arXiv:1907.05438] [INSPIRE].
A. Ball, E. Himwich, S.A. Narayanan, S. Pasterski and A. Strominger, Uplifting AdS3/CFT2 to flat space holography, JHEP 08 (2019) 168 [arXiv:1905.09809] [INSPIRE].
S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96 (2017) 065022 [arXiv:1705.01027] [INSPIRE].
A. Ashtekar, Asymptotic quantization: based on 1984 Naples lectures, Bibliopolis, Naples, Italy (1987).
C. Crnkovic and E. Witten, Covariant description of canonical formalism in geometrical theories, in Three hundred years of gravitation, S.W. Hawking and W. Israel eds., (1987), pg. 676.
J. Lee and R.M. Wald, Local symmetries and constraints, J. Math. Phys. 31 (1990) 725 [INSPIRE].
R.M. Wald and A. Zoupas, A general definition of ‘conserved quantities’ in general relativity and other theories of gravity, Phys. Rev. D 61 (2000) 084027 [gr-qc/9911095] [INSPIRE].
S. Weinberg, The quantum theory of fields. Volume 1: foundations, Cambridge University Press, Cambridge, U.K. (2005).
A. Strominger, Lectures on the infrared structure of gravity and gauge theory, Princeton University Press, Princeton, NJ, U.S.A. (2018) [arXiv:1703.05448] [INSPIRE].
G. Barnich and R. Ruzziconi, Coadjoint representation of the BMS group on celestial Riemann surfaces, JHEP 06 (2021) 079 [arXiv:2103.11253] [INSPIRE].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New symmetries of massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [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].
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, 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].
E. Himwich and A. Strominger, Celestial current algebra from Low’s subleading soft theorem, Phys. Rev. D 100 (2019) 065001 [arXiv:1901.01622] [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].
A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
S. Pasterski, A. Strominger and A. Zhiboedov, New gravitational memories, JHEP 12 (2016) 053 [arXiv:1502.06120] [INSPIRE].
L. Dolan, C.R. Nappi and E. Witten, Conformal operators for partially massless states, JHEP 10 (2001) 016 [hep-th/0109096] [INSPIRE].
C. Brust and K. Hinterbichler, Free □k scalar conformal field theory, JHEP 02 (2017) 066 [arXiv:1607.07439] [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].
E. Himwich, Z. Mirzaiyan and S. Pasterski, A note on the subleading soft graviton, JHEP 04 (2021) 172 [arXiv:1902.01840] [INSPIRE].
S. Stieberger and T.R. Taylor, Symmetries of celestial amplitudes, Phys. Lett. B 793 (2019) 141 [arXiv:1812.01080] [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].
E. Himwich, S.A. Narayanan, M. Pate, N. Paul and A. Strominger, The soft \( \mathcal{S} \)-matrix in gravity, JHEP 09 (2020) 129 [arXiv:2005.13433] [INSPIRE].
W. Fan, A. Fotopoulos, S. Stieberger and T.R. Taylor, On Sugawara construction on celestial sphere, JHEP 09 (2020) 139 [arXiv:2005.10666] [INSPIRE].
H.A. González, A. Puhm and F. Rojas, Loop corrections to celestial amplitudes, Phys. Rev. D 102 (2020) 126027 [arXiv:2009.07290] [INSPIRE].
L. Magnea, Non-Abelian infrared divergences on the celestial sphere, JHEP 05 (2021) 282 [arXiv:2104.10254] [INSPIRE].
H.A. González and F. Rojas, The structure of IR divergences in celestial gluon amplitudes, JHEP 21 (2021) 171 [arXiv:2104.12979] [INSPIRE].
A. Fotopoulos and T.R. Taylor, Primary fields in celestial CFT, JHEP 10 (2019) 167 [arXiv:1906.10149] [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].
G. Barnich and C. Troessaert, Supertranslations call for superrotations, PoS CNCFG2010 (2010) 010 [Ann. U. Craiova Phys. 21 (2011) S11] [arXiv:1102.4632] [INSPIRE].
N. Kalyanapuram, Soft gravity by squaring soft QED on the celestial sphere, Phys. Rev. D 103 (2021) 085016 [arXiv:2011.11412] [INSPIRE].
N. Kalyanapuram, Holographic soft S-matrix in QED and gravity, Phys. Rev. D 104 (2021) 045006 [arXiv:2105.04314] [INSPIRE].
A. Alekseev and S.L. Shatashvili, Path integral quantization of the coadjoint orbits of the Virasoro group and 2D gravity, Nucl. Phys. B 323 (1989) 719 [INSPIRE].
W. Fan, A. Fotopoulos, S. Stieberger, T.R. Taylor and B. Zhu, Conformal blocks from celestial gluon amplitudes, JHEP 05 (2021) 170 [arXiv:2103.04420] [INSPIRE].
E. Crawley, N. Miller, S.A. Narayanan and A. Strominger, State-operator correspondence in celestial conformal field theory, JHEP 09 (2021) 132 [arXiv:2105.00331] [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].
Y. Nakayama, Conformal equations that are not Virasoro or Weyl invariant, Lett. Math. Phys. 109 (2019) 2255 [arXiv:1902.05273] [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].
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Pasterski, S., Puhm, A. & Trevisani, E. Revisiting the conformally soft sector with celestial diamonds. J. High Energ. Phys. 2021, 143 (2021). https://doi.org/10.1007/JHEP11(2021)143
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DOI: https://doi.org/10.1007/JHEP11(2021)143