Abstract
The question of whether the holomorphic collinear singularities of graviton amplitudes define a consistent chiral algebra has garnered much recent attention. We analyse a version of this question for infinitesimal perturbations around the self-dual sector of 4d Einstein gravity. The singularities of tree amplitudes in such perturbations do form a consistent chiral algebra, however at 1-loop its operator products are corrected by the effective graviton vertex. We argue that the chiral algebra can be interpreted as the universal holomorphic surface defect in the twistor uplift of self-dual gravity, and show that the same correction is induced by an anomalous diagram in the bulk-defect system. The 1-loop holomorphic collinear singularities do not form a consistent chiral algebra. The failure of associativity can be traced to the existence of a recently discovered gravitational anomaly on twistor space. It can be restored by coupling to an unusual 4th-order gravitational axion, which cancels the anomaly by a Green-Schwarz mechanism. Alternatively, the anomaly vanishes in certain theories of self-dual gravity coupled to matter, including in self-dual supergravity.
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References
A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [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, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [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].
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].
R. Penrose, Twistor quantization and curved space-time, Int. J. Theor. Phys. 1 (1968) 61 [INSPIRE].
R. Penrose, Nonlinear Gravitons and Curved Twistor Theory, Gen. Rel. Grav. 7 (1976) 31 [INSPIRE].
T. Adamo, L. Mason and A. Sharma, Celestial w1+∞ Symmetries from Twistor Space, SIGMA 18 (2022) 016 [arXiv:2110.06066] [INSPIRE].
J.F. Plebanski, Some solutions of complex Einstein equations, J. Math. Phys. 16 (1975) 2395 [INSPIRE].
R. Capovilla, T. Jacobson, J. Dell and L.J. Mason, Selfdual two forms and gravity, Class. Quant. Grav. 8 (1991) 41 [INSPIRE].
L. Smolin, The GNewton → 0 limit of Euclidean quantum gravity, Class. Quant. Grav. 9 (1992) 883 [hep-th/9202076] [INSPIRE].
K. Krasnov, Self-Dual Gravity, Class. Quant. Grav. 34 (2017) 095001 [arXiv:1610.01457] [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].
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].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
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].
A. Brandhuber, S. McNamara, B. Spence and G. Travaglini, Recursion relations for one-loop gravity amplitudes, JHEP 03 (2007) 029 [hep-th/0701187] [INSPIRE].
S.D. Alston, D.C. Dunbar and W.B. Perkins, n-point amplitudes with a single negative-helicity graviton, Phys. Rev. D 92 (2015) 065024 [arXiv:1507.08882] [INSPIRE].
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, On-shell recurrence relations for one-loop QCD amplitudes, Phys. Rev. D 71 (2005) 105013 [hep-th/0501240] [INSPIRE].
S.D. Alston, D.C. Dunbar and W.B. Perkins, Complex Factorisation and Recursion for One-Loop Amplitudes, Phys. Rev. D 86 (2012) 085022 [arXiv:1208.0190] [INSPIRE].
D.C. Dunbar, J.H. Ettle and W.B. Perkins, Augmented Recursion For One-loop Gravity Amplitudes, JHEP 06 (2010) 027 [arXiv:1003.3398] [INSPIRE].
L.J. Mason and M. Wolf, Twistor Actions for Self-Dual Supergravities, Commun. Math. Phys. 288 (2009) 97 [arXiv:0706.1941] [INSPIRE].
A. Sharma, Twistor action for general relativity, arXiv:2104.07031 [INSPIRE].
R. Bittleston, A. Sharma and D. Skinner, Quantizing the non-linear graviton, arXiv:2208.12701 [INSPIRE].
M. Luscher, Quantum Nonlocal Charges and Absence of Particle Production in the Two-Dimensional Nonlinear Sigma Model, Nucl. Phys. B 135 (1978) 1 [INSPIRE].
M. Luscher and K. Pohlmeyer, Scattering of Massless Lumps and Nonlocal Charges in the Two-Dimensional Classical Nonlinear Sigma Model, Nucl. Phys. B 137 (1978) 46 [INSPIRE].
E. Brezin, C. Itzykson, J. Zinn-Justin and J.B. Zuber, Remarks About the Existence of Nonlocal Charges in Two-Dimensional Models, Phys. Lett. B 82 (1979) 442 [INSPIRE].
D. Bernard, Hidden Yangians in 2-D massive current algebras, Commun. Math. Phys. 137 (1991) 191 [INSPIRE].
K. Costello and M. Yamazaki, Gauge Theory And Integrability, III, arXiv:1908.02289 [INSPIRE].
R. Bittleston and D. Skinner, Twistors, the ASD Yang-Mills equations, and 4d Chern-Simons theory, arXiv:2011.04638 [INSPIRE].
L.C. Biedenharn and J.D. Louck, An intrinsically self-conjugate boson structure: The symplecton, Annals Phys. 63 (1971) 459 [INSPIRE].
R. Monteiro, Celestial chiral algebras, colour-kinematics duality and integrability, arXiv:2208.11179 [INSPIRE].
W. Bu, S. Heuveline and D. Skinner, Moyal deformations, W1+∞ and celestial holography, JHEP 12 (2022) 011 [arXiv:2208.13750] [INSPIRE].
C.N. Pope, Lectures on W algebras and W gravity, in Summer School in High-energy Physics and Cosmology, Trieste Italy, June 17 – August 9 1991, pp. 827–867 [hep-th/9112076] [INSPIRE].
X. Shen, W infinity and string theory, Int. J. Mod. Phys. A 7 (1992) 6953 [hep-th/9202072] [INSPIRE].
K.J. Costello, Quantizing local holomorphic field theories on twistor space, arXiv:2111.08879 [INSPIRE].
R.S. Ward, On Selfdual gauge fields, Phys. Lett. A 61 (1977) 81 [INSPIRE].
M.F. Atiyah, N.J. Hitchin and I.M. Singer, Selfduality in Four-Dimensional Riemannian Geometry, Proc. Roy. Soc. Lond. A 362 (1978) 425 [INSPIRE].
T. Adamo and L. Mason, Conformal and Einstein gravity from twistor actions, Class. Quant. Grav. 31 (2014) 045014 [arXiv:1307.5043] [INSPIRE].
T. Adamo, Twistor actions for gauge theory and gravity, arXiv:1308.2820 [INSPIRE].
D. Skinner, Twistor strings for \( \mathcal{N} \) = 8 supergravity, JHEP 04 (2020) 047 [arXiv:1301.0868] [INSPIRE].
K. Krasnov and E. Skvortsov, Flat self-dual gravity, JHEP 08 (2021) 082 [arXiv:2106.01397] [INSPIRE].
A. Ashtekar, T. Jacobson and L. Smolin, A New Characterization of Half Flat Solutions to Einstein’s Equation, Commun. Math. Phys. 115 (1988) 631 [INSPIRE].
B.R. Williams, Renormalization for holomorphic field theories, Commun. Math. Phys. 374 (2020) 1693 [arXiv:1809.02661] [INSPIRE].
C. Elliott and B.R. Williams, Holomorphic Poisson Field Theories, arXiv:2008.02302 [INSPIRE].
N.M. Paquette and B.R. Williams, Koszul duality in quantum field theory, arXiv:2110.10257 [INSPIRE].
K. Costello and S. Li, Anomaly cancellation in the topological string, Adv. Theor. Math. Phys. 24 (2020) 1723 [arXiv:1905.09269] [INSPIRE].
W.A. Bardeen, Selfdual Yang-Mills theory, integrability and multiparton amplitudes, Prog. Theor. Phys. Suppl. 123 (1996) 1 [INSPIRE].
L. Mason, Local twistors and the Penrose tranform for homogeneous bundles, Twistor Newslett. 23 (1987) 36.
Z. Bern, L.J. Dixon, M. Perelstein and J.S. Rozowsky, One loop n point helicity amplitudes in (selfdual) gravity, Phys. Lett. B 444 (1998) 273 [hep-th/9809160] [INSPIRE].
D.C. Dunbar, J.H. Ettle and W.B. Perkins, Obtaining One-loop Gravity Amplitudes Using Spurious Singularities, Phys. Rev. D 84 (2011) 125029 [arXiv:1109.4827] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [INSPIRE].
N.E.J. Bjerrum-Bohr, D.C. Dunbar, H. Ita, W.B. Perkins and K. Risager, MHV-vertices for gravity amplitudes, JHEP 01 (2006) 009 [hep-th/0509016] [INSPIRE].
L.J. Mason and D. Skinner, Gravity, Twistors and the MHV Formalism, Commun. Math. Phys. 294 (2010) 827 [arXiv:0808.3907] [INSPIRE].
P. Benincasa, C. Boucher-Veronneau and F. Cachazo, Taming Tree Amplitudes In General Relativity, JHEP 11 (2007) 057 [hep-th/0702032] [INSPIRE].
M. Bianchi, H. Elvang and D.Z. Freedman, Generating tree amplitudes in \( \mathcal{N} \) = 4 SYM and \( \mathcal{N} \) = 8 SG, JHEP 09 (2008) 063 [arXiv:0805.0757] [INSPIRE].
E. Conde and S. Rajabi, The Twelve-Graviton Next-to-MHV Amplitude from Risager’s Construction, JHEP 09 (2012) 120 [arXiv:1205.3500] [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].
R. Bhardwaj, L. Lippstreu, L. Ren, M. Spradlin, A. Yelleshpur Srikant and A. Volovich, Loop-level gluon OPEs in celestial holography, JHEP 11 (2022) 171 [arXiv:2208.14416] [INSPIRE].
Q.-H. Park, Selfdual Gravity as a Large N Limit of the Two-dimensional Nonlinear σ Model, Phys. Lett. B 238 (1990) 287 [INSPIRE].
K. Takasaki, Symmetries of Hyper-Kähler (or Poisson gauge field) hierarchy, J. Math. Phys. 31 (1990) 1877 [INSPIRE].
M. Dunajski and L.J. Mason, Hyper-Kähler hierarchies and their twistor theory, Commun. Math. Phys. 213 (2000) 641 [math/0001008] [INSPIRE].
N.M.J. Woodhouse, Real methods in twistor theory, Class. Quant. Grav. 2 (1985) 257 [INSPIRE].
M.T. Grisaru, H.N. Pendleton and P. van Nieuwenhuizen, Supergravity and the S Matrix, Phys. Rev. D 15 (1977) 996 [INSPIRE].
M.T. Grisaru and H.N. Pendleton, Some Properties of Scattering Amplitudes in Supersymmetric Theories, Nucl. Phys. B 124 (1977) 81 [INSPIRE].
S.J. Parke and T.R. Taylor, Perturbative QCD Utilizing Extended Supersymmetry, Phys. Lett. B 157 (1985) 81 [INSPIRE].
W. Bu and E. Casali, The 4d/2d correspondence in twistor space and holomorphic Wilson lines, JHEP 11 (2022) 076 [arXiv:2208.06334] [INSPIRE].
A. Guevara, Towards Gravity From a Color Symmetry, arXiv:2209.00696 [INSPIRE].
R.S. Ward, Self-dual space-times with cosmological constant, Commun. Math. Phys. 78 (1980) 1 [INSPIRE].
H. Ooguri and C. Vafa, Selfduality and \( \mathcal{N} \) = 2 String magic, Mod. Phys. Lett. A 5 (1990) 1389 [INSPIRE].
H. Ooguri and C. Vafa, Geometry of \( \mathcal{N} \) = 2 strings, Nucl. Phys. B 361 (1991) 469 [INSPIRE].
K. Costello, M-theory in the Omega-background and 5-dimensional non-commutative gauge theory, arXiv:1610.04144 [INSPIRE].
K. Costello, Holography and Koszul duality: the example of the M 2 brane, arXiv:1705.02500 [INSPIRE].
D. Gaiotto and J. Oh, Aspects of Ω-deformed M-theory, arXiv:1907.06495 [INSPIRE].
J. Oh and Y. Zhou, Feynman diagrams and Ω-deformed M-theory, SciPost Phys. 10 (2021) 029 [arXiv:2002.07343] [INSPIRE].
D. Gaiotto and J. Abajian, Twisted M2 brane holography and sphere correlation functions, arXiv:2004.13810 [INSPIRE].
K. Costello, N.M. Paquette and A. Sharma, Top-down holography in an asymptotically flat spacetime, arXiv:2208.14233 [INSPIRE].
T. Adamo, L. Mason and A. Sharma, Twistor sigma models for quaternionic geometry and graviton scattering, arXiv:2103.16984 [INSPIRE].
L.J. Dixon, A brief introduction to modern amplitude methods, in Theoretical Advanced Study Institute in Elementary Particle Physics: Particle Physics: The Higgs Boson and Beyond, Boulder U.S.A., June 3–28 2013, pp. 31–67 [DOI] [arXiv:1310.5353] [INSPIRE].
Z. Bern, D.C. Dunbar and T. Shimada, String based methods in perturbative gravity, Phys. Lett. B 312 (1993) 277 [hep-th/9307001] [INSPIRE].
D.C. Dunbar and P.S. Norridge, Calculation of graviton scattering amplitudes using string based methods, Nucl. Phys. B 433 (1995) 181 [hep-th/9408014] [INSPIRE].
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Bittleston, R. On the associativity of 1-loop corrections to the celestial operator product in gravity. J. High Energ. Phys. 2023, 18 (2023). https://doi.org/10.1007/JHEP01(2023)018
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DOI: https://doi.org/10.1007/JHEP01(2023)018