Abstract
Recent works have explored how scattering amplitudes in quantum self-dual Yang-Mills theory and self-dual gravity can be interpreted as resulting from an anomaly, as first proposed by W. Bardeen. We study this problem in the light-cone-gauge formulation of the theories. Firstly, we describe how the infinite tower of symmetries associated to classical integrability can be quantum corrected, exhibiting the one-loop anomaly. Secondly, we present quantum-corrected light-cone Lagrangians worthy of the simplicity of the amplitudes, building on recent works describing the anomaly in twistor space. Finally, we discover an unexpected BCJ-like double copy for the (loop-integrated) amplitudes, distinct from the well-known BCJ double copy for the loop integrands.
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References
Z. Bern, G. Chalmers, L.J. Dixon and D.A. Kosower, One loop N gluon amplitudes with maximal helicity violation via collinear limits, Phys. Rev. Lett. 72 (1994) 2134 [hep-ph/9312333] [INSPIRE].
G. Mahlon, Multi-gluon helicity amplitudes involving a quark loop, Phys. Rev. D 49 (1994) 4438 [hep-ph/9312276] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop selfdual and N = 4 superYang-Mills, Phys. Lett. B 394 (1997) 105 [hep-th/9611127] [INSPIRE].
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].
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. Cangemi, Selfdual Yang-Mills theory and one loop like-helicity QCD multi-gluon amplitudes, Nucl. Phys. B 484 (1997) 521 [hep-th/9605208] [INSPIRE].
G. Chalmers and W. Siegel, The Selfdual sector of QCD amplitudes, Phys. Rev. D 54 (1996) 7628 [hep-th/9606061] [INSPIRE].
W.A. Bardeen, Selfdual Yang-Mills theory, integrability and multiparton amplitudes, Prog. Theor. Phys. Suppl. 123 (1996) 1 [INSPIRE].
K.J. Costello, Quantizing local holomorphic field theories on twistor space, arXiv:2111.08879 [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].
R. Bittleston, A. Sharma and D. Skinner, Quantizing the non-linear graviton, arXiv:2208.12701 [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].
K. Costello, N.M. Paquette and A. Sharma, Top-Down Holography in an Asymptotically Flat Spacetime, Phys. Rev. Lett. 130 (2023) 061602 [arXiv:2208.14233] [INSPIRE].
R. Bittleston, On the associativity of 1-loop corrections to the celestial operator product in gravity, JHEP 01 (2023) 018 [arXiv:2211.06417] [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].
H. Jiang, Holographic chiral algebra: supersymmetry, infinite Ward identities, and EFTs, JHEP 01 (2022) 113 [arXiv:2108.08799] [INSPIRE].
H. Jiang, Celestial OPEs and w1+∞ algebra from worldsheet in string theory, JHEP 01 (2022) 101 [arXiv:2110.04255] [INSPIRE].
T. Adamo, L. Mason and A. Sharma, Celestial w1+∞ Symmetries from Twistor Space, SIGMA 18 (2022) 016 [arXiv:2110.06066] [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].
J. Mago, L. Ren, A.Y. Srikant and A. Volovich, Deformed w1+∞ Algebras in the Celestial CFT, SIGMA 19 (2023) 044 [arXiv:2111.11356] [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. Monteiro, Celestial chiral algebras, colour-kinematics duality and integrability, JHEP 01 (2023) 092 [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].
R. Bhardwaj et al., Loop-level gluon OPEs in celestial holography, JHEP 11 (2022) 171 [arXiv:2208.14416] [INSPIRE].
A. Guevara, Towards Gravity From a Color Symmetry, arXiv:2209.00696 [INSPIRE].
A. Ball, Celestial locality and the Jacobi identity, JHEP 01 (2023) 146 [arXiv:2211.09151] [INSPIRE].
T. Adamo, Lectures on twistor theory, PoS Modave2017 (2018) 003 [arXiv:1712.02196] [INSPIRE].
L.J. Mason and N. Woodhouse, Integrability, Self-duality, and Twistor Theory, London Mathematical Society monographs, Clarendon Press (1996) [ISBN: 9780198534983] [INSPIRE].
M. Dunajski, Solitons, instantons, and twistors, Oxford Univerity Press (2010) [ISBN: 9780198570622] [INSPIRE].
A.A. Rosly and K.G. Selivanov, On amplitudes in selfdual sector of Yang-Mills theory, Phys. Lett. B 399 (1997) 135 [hep-th/9611101] [INSPIRE].
A. Brandhuber, B. Spence and G. Travaglini, Amplitudes in Pure Yang-Mills and MHV Diagrams, JHEP 02 (2007) 088 [hep-th/0612007] [INSPIRE].
A. Brandhuber, B. Spence, G. Travaglini and K. Zoubos, One-loop MHV Rules and Pure Yang-Mills, JHEP 07 (2007) 002 [arXiv:0704.0245] [INSPIRE].
R. Boels and C. Schwinn, Deriving CSW rules for massive scalar legs and pure Yang-Mills loops, JHEP 07 (2008) 007 [arXiv:0805.1197] [INSPIRE].
K. Krasnov, Self-Dual Gravity, Class. Quant. Grav. 34 (2017) 095001 [arXiv:1610.01457] [INSPIRE].
D. Nandan, J. Plefka and G. Travaglini, All rational one-loop Einstein-Yang-Mills amplitudes at four points, JHEP 09 (2018) 011 [arXiv:1803.08497] [INSPIRE].
P. Chattopadhyay and K. Krasnov, One-loop same helicity four-point amplitude from shifts, JHEP 06 (2020) 082 [arXiv:2002.11390] [INSPIRE].
P. Chattopadhyay and K. Krasnov, One-loop same helicity YM amplitudes from BG currents, JHEP 03 (2022) 191 [arXiv:2110.00331] [INSPIRE].
W. Siegel, Selfdual N=8 supergravity as closed N = 2 (N = 4) strings, Phys. Rev. D 47 (1993) 2504 [hep-th/9207043] [INSPIRE].
K. Lee, Quantum off-shell recursion relation, JHEP 05 (2022) 051 [arXiv:2202.08133] [INSPIRE].
H. Gomez, R. Lipinski Jusinskas, C. Lopez-Arcos and A. Quintero Velez, One-Loop Off-Shell Amplitudes from Classical Equations of Motion, Phys. Rev. Lett. 130 (2023) 081601 [arXiv:2208.02831] [INSPIRE].
H. Kakkad, P. Kotko and A. Stasto, One-Loop effective action approach to quantum MHV theory, JHEP 11 (2022) 132 [arXiv:2208.11000] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
Z. Bern et al., The Duality Between Color and Kinematics and its Applications, arXiv:1909.01358 [INSPIRE].
R. Monteiro and D. O’Connell, The Kinematic Algebra From the Self-Dual Sector, JHEP 07 (2011) 007 [arXiv:1105.2565] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
R.H. Boels, R.S. Isermann, R. Monteiro and D. O’Connell, Colour-Kinematics Duality for One-Loop Rational Amplitudes, JHEP 04 (2013) 107 [arXiv:1301.4165] [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].
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].
M. Campiglia and S. Nagy, A double copy for asymptotic symmetries in the self-dual sector, JHEP 03 (2021) 262 [arXiv:2102.01680] [INSPIRE].
C. Cheung and J. Mangan, Covariant color-kinematics duality, JHEP 11 (2021) 069 [arXiv:2108.02276] [INSPIRE].
A. Brandhuber et al., Kinematic Hopf Algebra for Bern-Carrasco-Johansson Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory, Phys. Rev. Lett. 128 (2022) 121601 [arXiv:2111.15649] [INSPIRE].
G. Chen, G. Lin and C. Wen, Kinematic Hopf algebra for amplitudes and form factors, Phys. Rev. D 107 (2023) L081701 [arXiv:2208.05519] [INSPIRE].
A. Brandhuber et al., Amplitudes, Hopf algebras and the colour-kinematics duality, JHEP 12 (2022) 101 [arXiv:2208.05886] [INSPIRE].
Q. Cao, J. Dong, S. He and Y.-Q. Zhang, Covariant color-kinematics duality, Hopf algebras, and permutohedra, Phys. Rev. D 107 (2023) 026022 [arXiv:2211.05404] [INSPIRE].
Z. Bern et al., The SAGEX review on scattering amplitudes Chapter 2: An invitation to color-kinematics duality and the double copy, J. Phys. A 55 (2022) 443003 [arXiv:2203.13013] [INSPIRE].
D.A. Kosower, R. Monteiro and D. O’Connell, The SAGEX review on scattering amplitudes Chapter 14: Classical gravity from scattering amplitudes, J. Phys. A 55 (2022) 443015 [arXiv:2203.13025] [INSPIRE].
T. Adamo et al., Snowmass White Paper: the Double Copy and its Applications, in the proceedings of the Snowmass 2021, Seattle U.S.A., July 17–26 (2022) [arXiv:2204.06547] [INSPIRE].
C.R. Mafra and O. Schlotterer, Tree-level amplitudes from the pure spinor superstring, Phys. Rept. 1020 (2023) 1 [arXiv:2210.14241] [INSPIRE].
M.K. Prasad, A. Sinha and L.-L. Wang, Nonlocal Continuity Equations for Selfdual SU(N) Yang-Mills Fields, Phys. Lett. B 87 (1979) 237 [INSPIRE].
L. Dolan, Kac-moody Algebras and Exact Solvability in Hadronic Physics, Phys. Rept. 109 (1984) 1 [INSPIRE].
R.S. Ward, Integrable and solvable systems, and relations among them, Phil. Trans. Roy. Soc. Lond. A 315 (1985) 451 [INSPIRE].
E. Chacón et al., New heavenly double copies, JHEP 03 (2021) 247 [arXiv:2008.09603] [INSPIRE].
C.B. Thorn, Renormalization of quantum fields on the lightcone worldsheet. I. Scalar fields, Nucl. Phys. B 699 (2004) 427 [hep-th/0405018] [INSPIRE].
K. Bardakci and C.B. Thorn, A Mean field approximation to the world sheet model of planar ϕ3 field theory, Nucl. Phys. B 652 (2003) 196 [hep-th/0206205] [INSPIRE].
D. Chakrabarti, J. Qiu and C.B. Thorn, Scattering of glue by glue on the light-cone worldsheet. I. Helicity non-conserving amplitudes, Phys. Rev. D 72 (2005) 065022 [hep-th/0507280] [INSPIRE].
R. Boels, A Quantization of twistor Yang-Mills theory through the background field method, Phys. Rev. D 76 (2007) 105027 [hep-th/0703080] [INSPIRE].
H. Feng and Y.-T. Huang, MHV Lagrangian for N = 4 super Yang-Mills, JHEP 04 (2009) 047 [hep-th/0611164] [INSPIRE].
F. Cachazo, P. Svrcek and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP 09 (2004) 006 [hep-th/0403047] [INSPIRE].
P. Mansfield, The Lagrangian origin of MHV rules, JHEP 03 (2006) 037 [hep-th/0511264] [INSPIRE].
N.E.J. Bjerrum-Bohr, T. Dennen, R. Monteiro and D. O’Connell, Integrand Oxidation and One-Loop Colour-Dual Numerators in N = 4 Gauge Theory, JHEP 07 (2013) 092 [arXiv:1303.2913] [INSPIRE].
Z. Bern et al., Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops, Phys. Rev. D 92 (2015) 045041 [arXiv:1303.6605] [INSPIRE].
C.R. Mafra and O. Schlotterer, Towards one-loop SYM amplitudes from the pure spinor BRST cohomology, Fortsch. Phys. 63 (2015) 105 [arXiv:1410.0668] [INSPIRE].
Y. Geyer, L. Mason, R. Monteiro and P. Tourkine, Loop Integrands for Scattering Amplitudes from the Riemann Sphere, Phys. Rev. Lett. 115 (2015) 121603 [arXiv:1507.00321] [INSPIRE].
Y. Geyer, L. Mason, R. Monteiro and P. Tourkine, One-loop amplitudes on the Riemann sphere, JHEP 03 (2016) 114 [arXiv:1511.06315] [INSPIRE].
S. He, R. Monteiro and O. Schlotterer, String-inspired BCJ numerators for one-loop MHV amplitudes, JHEP 01 (2016) 171 [arXiv:1507.06288] [INSPIRE].
S. He and O. Schlotterer, New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level, Phys. Rev. Lett. 118 (2017) 161601 [arXiv:1612.00417] [INSPIRE].
Z. Bern et al., Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes, Phys. Rev. Lett. 118 (2017) 181602 [arXiv:1701.02519] [INSPIRE].
S. He, O. Schlotterer and Y. Zhang, New BCJ representations for one-loop amplitudes in gauge theories and gravity, Nucl. Phys. B 930 (2018) 328 [arXiv:1706.00640] [INSPIRE].
C.R. Mafra and O. Schlotterer, Double-Copy Structure of One-Loop Open-String Amplitudes, Phys. Rev. Lett. 121 (2018) 011601 [arXiv:1711.09104] [INSPIRE].
C.R. Mafra and O. Schlotterer, Towards the n-point one-loop superstring amplitude. Part III. One-loop correlators and their double-copy structure, JHEP 08 (2019) 092 [arXiv:1812.10971] [INSPIRE].
A. Edison, S. He, O. Schlotterer and F. Teng, One-loop Correlators and BCJ Numerators from Forward Limits, JHEP 09 (2020) 079 [arXiv:2005.03639] [INSPIRE].
E. Bridges and C.R. Mafra, Local BCJ numerators for ten-dimensional SYM at one loop, JHEP 07 (2021) 031 [arXiv:2102.12943] [INSPIRE].
F. Porkert and O. Schlotterer, One-loop amplitudes in Einstein-Yang-Mills from forward limits, JHEP 02 (2023) 122 [arXiv:2201.12072] [INSPIRE].
A. Edison et al., Perfecting one-loop BCJ numerators in SYM and supergravity, JHEP 02 (2023) 164 [arXiv:2211.00638] [INSPIRE].
S.D. Badger, Direct Extraction Of One Loop Rational Terms, JHEP 01 (2009) 049 [arXiv:0806.4600] [INSPIRE].
Z. Bern, H.-H. Chi, L. Dixon and A. Edison, Two-Loop Renormalization of Quantum Gravity Simplified, Phys. Rev. D 95 (2017) 046013 [arXiv:1701.02422] [INSPIRE].
J.J.M. Carrasco, R. Kallosh, R. Roiban and A.A. Tseytlin, On the U(1) duality anomaly and the S-matrix of N = 4 supergravity, JHEP 07 (2013) 029 [arXiv:1303.6219] [INSPIRE].
Z. Bern et al., Ultraviolet Properties of N = 4 Supergravity at Four Loops, Phys. Rev. Lett. 111 (2013) 231302 [arXiv:1309.2498] [INSPIRE].
Z. Bern, J. Parra-Martinez and R. Roiban, Canceling the U(1) Anomaly in the S Matrix of N = 4 Supergravity, Phys. Rev. Lett. 121 (2018) 101604 [arXiv:1712.03928] [INSPIRE].
Z. Bern, D. Kosower and J. Parra-Martinez, Two-loop n-point anomalous amplitudes in N = 4 supergravity, Proc. Roy. Soc. Lond. A 476 (2020) 20190722 [arXiv:1905.05151] [INSPIRE].
J.J.M. Carrasco, M. Lewandowski and N.H. Pavao, Color-Dual Fates of F3, R3, and N = 4 Supergravity, Phys. Rev. Lett. 131 (2023) 051601 [arXiv:2203.03592] [INSPIRE].
R. Britto, G.R. Jehu and A. Orta, The dimension-shift conjecture for one-loop amplitudes, JHEP 04 (2021) 276 [arXiv:2011.13821] [INSPIRE].
J. Henn, B. Power and S. Zoia, Conformal Invariance of the One-Loop All-Plus Helicity Scattering Amplitudes, JHEP 02 (2020) 019 [arXiv:1911.12142] [INSPIRE].
J. Faller and J. Plefka, Positive helicity Einstein-Yang-Mills amplitudes from the double copy method, Phys. Rev. D 99 (2019) 046008 [arXiv:1812.04053] [INSPIRE].
D. Ponomarev and E.D. Skvortsov, Light-Front Higher-Spin Theories in Flat Space, J. Phys. A 50 (2017) 095401 [arXiv:1609.04655] [INSPIRE].
D. Ponomarev, Chiral Higher Spin Theories and Self-Duality, JHEP 12 (2017) 141 [arXiv:1710.00270] [INSPIRE].
K. Krasnov, E. Skvortsov and T. Tran, Actions for self-dual Higher Spin Gravities, JHEP 08 (2021) 076 [arXiv:2105.12782] [INSPIRE].
T. Tran, Twistor constructions for higher-spin extensions of (self-dual) Yang-Mills, JHEP 11 (2021) 117 [arXiv:2107.04500] [INSPIRE].
E. Skvortsov and R. Van Dongen, Minimal models of field theories: Chiral higher spin gravity, Phys. Rev. D 106 (2022) 045006 [arXiv:2204.10285] [INSPIRE].
A. Sharapov et al., Minimal model of Chiral Higher Spin Gravity, JHEP 09 (2022) 134 [Erratum ibid. 02 (2023) 183] [arXiv:2205.07794] [INSPIRE].
T. Tran, Toward a twistor action for chiral higher-spin gravity, Phys. Rev. D 107 (2023) 046015 [arXiv:2209.00925] [INSPIRE].
Y. Herfray, K. Krasnov and E. Skvortsov, Higher-spin self-dual Yang-Mills and gravity from the twistor space, JHEP 01 (2023) 158 [arXiv:2210.06209] [INSPIRE].
T. Adamo and T. Tran, Higher-spin Yang–Mills, amplitudes and self-duality, Lett. Math. Phys. 113 (2023) 50 [arXiv:2210.07130] [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, H. Johansson and T. Sondergaard, Monodromy-like Relations for Finite Loop Amplitudes, JHEP 05 (2011) 039 [arXiv:1103.6190] [INSPIRE].
E. Blanco, A. van Hameren, P. Kotko and K. Kutak, All-plus helicity off-shell gauge invariant multigluon amplitudes at one loop, JHEP 12 (2020) 158 [arXiv:2008.07916] [INSPIRE].
Acknowledgments
We thank Zvi Bern, Andi Brandhuber, Graham Brown, Josh Gowdy, Lionel Mason, Natalie Paquette, Atul Sharma, Gabriele Travaglini and Chris White for discussions and comments. RM is supported by the Royal Society via a University Research Fellowship. RSM was supported by the Royal Society via a studentship grant. SW’s studentship is supported by STFC.
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Monteiro, R., Stark-Muchão, R. & Wikeley, S. Anomaly and double copy in quantum self-dual Yang-Mills and gravity. J. High Energ. Phys. 2023, 30 (2023). https://doi.org/10.1007/JHEP09(2023)030
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DOI: https://doi.org/10.1007/JHEP09(2023)030