Abstract
The Cachazo-Strominger subleading soft graviton theorem for a positive helicity soft graviton is equivalent to the Ward identities for \( \overline{\mathrm{SL}\left(2,\mathrm{\mathbb{C}}\right)} \) currents. This naturally gives rise to a \( \overline{\mathrm{SL}\left(2,\mathrm{\mathbb{C}}\right)} \) current algebra living on the celestial sphere. The generators of the \( \overline{\mathrm{SL}\left(2,\mathrm{\mathbb{C}}\right)} \) current algebra and the supertranslations, coming from a positive helicity leading soft graviton, form a closed algebra. We find that the OPE of two graviton primaries in the Celestial CFT, extracted from MHV amplitudes, is completely determined in terms of this algebra. To be more precise, 1) The subleading terms in the OPE are determined in terms of the leading OPE coefficient if we demand that both sides of the OPE transform in the same way under this local symmetry algebra. 2) Positive helicity gravitons have null states under this local algebra whose decoupling leads to differential equations for MHV amplitudes. An n point MHV amplitude satisfies two systems of (n − 2) linear first order PDEs corresponding to (n − 2) positive helicity gravitons. We have checked, using Hodges’ formula, that one system of differential equations is satisfied by any MHV amplitude, whereas the other system has been checked up to six graviton MHV amplitude. 3) One can determine the leading OPE coefficients from these differential equations.
This points to the existence of an autonomous sector of the Celestial CFT which holographically computes the MHV graviton scattering amplitudes and is completely defined by this local symmetry algebra. The MHV-sector of the Celestial CFT is like a minimal model of 2-D CFT.
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References
F. Cachazo and A. Strominger, Evidence for a new soft graviton theorem, arXiv:1404.4091 [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].
M. Pate, A.-M. Raclariu, A. Strominger and E. Y. Yuan, Celestial operator products of gluons and gravitons, arXiv:1910.07424 [INSPIRE].
Y. T. A. Law and M. Zlotnikov, Poincaré constraints on celestial amplitudes, JHEP 03 (2020) 085 [Erratum ibid. 04 (2020) 202] [arXiv:1910.04356] [INSPIRE].
S. Banerjee, S. Ghosh and R. Gonzo, BMS symmetry of celestial OPE, JHEP 04 (2020) 130 [arXiv:2002.00975] [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. 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].
A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448 [INSPIRE].
D. Kapec, V. Lysov, S. Pasterski and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity 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].
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].
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].
H. Bondi, M. G. J. van der Burg and A. W. K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
R. K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A 270 (1962) 103 [INSPIRE].
R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128 (1962) 2851 [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 (2010) [arXiv:1102.4632] [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].
A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90 (2014) 124028 [arXiv:1408.2228] [INSPIRE].
L. Donnay, S. Pasterski and A. Puhm, Asymptotic symmetries and celestial CFT, JHEP 09 (2020) 176 [arXiv:2005.08990] [INSPIRE].
M. Campiglia and J. Peraza, Generalized BMS charge algebra, Phys. Rev. D 101 (2020) 104039 [arXiv:2002.06691] [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].
D. Kapec and P. Mitra, A d-dimensional stress tensor for Minkd+2 gravity, JHEP 05 (2018) 186 [arXiv:1711.04371] [INSPIRE].
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].
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].
J. de Boer and S. N. Solodukhin, A holographic reduction of Minkowski space-time, Nucl. Phys. B 665 (2003) 545 [hep-th/0303006] [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, S. Ghosh, P. Pandey and A. P. Saha, Modified celestial amplitude in Einstein gravity, JHEP 03 (2020) 125 [arXiv:1909.03075] [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].
A. Schreiber, A. Volovich and M. Zlotnikov, Tree-level gluon amplitudes on the celestial sphere, Phys. Lett. B 781 (2018) 349 [arXiv:1711.08435] [INSPIRE].
C. Cardona and Y.-T. Huang, S-matrix singularities and CFT correlation functions, JHEP 08 (2017) 133 [arXiv:1702.03283] [INSPIRE].
H. T. Lam and S.-H. Shao, Conformal basis, optical theorem, and the bulk point singularity, Phys. Rev. D 98 (2018) 025020 [arXiv:1711.06138] [INSPIRE].
N. Banerjee, S. Banerjee, S. Atul Bhatkar and S. Jain, Conformal structure of massless scalar amplitudes beyond tree level, JHEP 04 (2018) 039 [arXiv:1711.06690] [INSPIRE].
S. Stieberger and T. R. Taylor, Strings on celestial sphere, Nucl. Phys. B 935 (2018) 388 [arXiv:1806.05688] [INSPIRE].
S. Stieberger and T. R. Taylor, Symmetries of celestial amplitudes, Phys. Lett. B 793 (2019) 141 [arXiv:1812.01080] [INSPIRE].
S. Banerjee, P. Pandey and P. Paul, Conformal properties of soft operators. Part I. 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].
A. Fotopoulos and T. R. Taylor, Primary fields in celestial CFT, JHEP 10 (2019) 167 [arXiv:1906.10149] [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].
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].
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].
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].
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].
A. Bagchi, R. Basu, A. Kakkar and A. Mehra, Flat holography: aspects of the dual field theory, JHEP 12 (2016) 147 [arXiv:1609.06203] [INSPIRE].
A. Hodges, New expressions for gravitational scattering amplitudes, JHEP 07 (2013) 075 [arXiv:1108.2227] [INSPIRE].
A. Hodges, A simple formula for gravitational MHV amplitudes, arXiv:1204.1930 [INSPIRE].
P. Paul, unpublished work.
Z. Bern, L. J. Dixon, M. Perelstein and J. S. Rozowsky, Multileg one loop gravity amplitudes from gauge theory, Nucl. Phys. B 546 (1999) 423 [hep-th/9811140] [INSPIRE].
D. Nandan, J. Plefka and W. Wormsbecher, Collinear limits beyond the leading order from the scattering equations, JHEP 02 (2017) 038 [arXiv:1608.04730] [INSPIRE].
L. Rodina, Scattering amplitudes from soft theorems and infrared behavior, Phys. Rev. Lett. 122 (2019) 071601 [arXiv:1807.09738] [INSPIRE].
S. Banerjee, S. Ghosh, P. Pandey, P. Paul and A. P. Saha, unpublished work.
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Banerjee, S., Ghosh, S. & Paul, P. MHV graviton scattering amplitudes and current algebra on the celestial sphere. J. High Energ. Phys. 2021, 176 (2021). https://doi.org/10.1007/JHEP02(2021)176
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DOI: https://doi.org/10.1007/JHEP02(2021)176