Abstract
On-shell kinematics for gluon scattering can be parametrized with points on the celestial sphere; in the limit where these points collide, it is known that tree-level gluon scattering amplitudes exhibit an operator product expansion (OPE)-like structure. While it is possible to obtain singular contributions to this celestial OPE, getting regular contributions from both holomorphic and anti-holomorphic sectors is more difficult. In this paper, we use twistor string theory to describe the maximal helicity violating (MHV) sector of tree-level, four-dimensional gluon scattering as an effective 2d conformal field theory on the celestial sphere. By organizing the OPE between vertex operators in this theory in terms of soft gluon descendants, we obtain all-order expressions for the celestial OPE which include all regular contributions in the collinear expansion. This gives new, all-order formulae for the collinear splitting function (in momentum space) and celestial OPE coefficients (in the conformal primary basis) of tree-level MHV gluon scattering. We obtain these results for both positive and negative helicity gluons, and for any incoming/outgoing kinematic configuration within the MHV sector.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].
M.L. Mangano and S.J. Parke, Multiparton amplitudes in gauge theories, Phys. Rept. 200 (1991) 301 [hep-th/0509223] [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].
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].
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].
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].
S. Pasterski, M. Pate and A.-M. Raclariu, Celestial Holography, in 2022 Snowmass Summer Study, Seattle, U.S.A. (2021) [arXiv:2111.11392] [INSPIRE].
T. McLoughlin, A. Puhm and A.-M. Raclariu, The SAGEX review on scattering amplitudes chapter 11: soft theorems and celestial amplitudes, J. Phys. A 55 (2022) 443012 [arXiv:2203.13022] [INSPIRE].
E. Himwich, M. Pate and K. Singh, Celestial operator product expansions and w1+∞ symmetry for all spins, JHEP 01 (2022) 080 [arXiv:2108.07763] [INSPIRE].
H. Jiang, Holographic chiral algebra: supersymmetry, infinite Ward identities, and EFTs, JHEP 01 (2022) 113 [arXiv:2108.08799] [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].
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].
A. Guevara, Celestial OPE blocks, arXiv:2108.12706 [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].
W. Fan, A. Fotopoulos, S. Stieberger, T.R. Taylor and B. Zhu, Conformal blocks from celestial gluon amplitudes. Part II. Single-valued correlators, JHEP 11 (2021) 179 [arXiv:2108.10337] [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].
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].
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].
A. Ball, Celestial locality and the Jacobi identity, JHEP 01 (2023) 146 [arXiv:2211.09151] [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].
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].
S. Banerjee, S. Ghosh and R. Gonzo, BMS symmetry of celestial OPE, JHEP 04 (2020) 130 [arXiv:2002.00975] [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. Ebert, A. Sharma and D. Wang, Descendants in celestial CFT and emergent multi-collinear factorization, JHEP 03 (2021) 030 [arXiv:2009.07881] [INSPIRE].
S. Banerjee and S. Ghosh, MHV gluon scattering amplitudes from celestial current algebras, JHEP 10 (2021) 111 [arXiv:2011.00017] [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].
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].
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
N. Berkovits, An Alternative string theory in twistor space for N = 4 superYang-Mills, Phys. Rev. Lett. 93 (2004) 011601 [hep-th/0402045] [INSPIRE].
E.T. Newman, Heaven and Its Properties, Gen. Rel. Grav. 7 (1976) 107 [INSPIRE].
R. Penrose, Nonlinear Gravitons and Curved Twistor Theory, Gen. Rel. Grav. 7 (1976) 31 [INSPIRE].
R.O. Hansen, E.T. Newman, R. Penrose and K.P. Tod, The Metric and Curvature Properties of H Space, Proc. Roy. Soc. Lond. A 363 (1978) 445 [INSPIRE].
M. Eastwood and P. Tod, Edth-a differential operator on the sphere, Math. Proc. Camb. Philos. Soc. 92 (1982) 317.
T. Adamo, E. Casali and D. Skinner, Perturbative gravity at null infinity, Class. Quant. Grav. 31 (2014) 225008 [arXiv:1405.5122] [INSPIRE].
Y. Geyer, A.E. Lipstein and L. Mason, Ambitwistor strings at null infinity and (subleading) soft limits, Class. Quant. Grav. 32 (2015) 055003 [arXiv:1406.1462] [INSPIRE].
T. Adamo and E. Casali, Perturbative gauge theory at null infinity, Phys. Rev. D 91 (2015) 125022 [arXiv:1504.02304] [INSPIRE].
T. Adamo, L. Mason and A. Sharma, Celestial w1+∞ Symmetries from Twistor Space, SIGMA 18 (2022) 016 [arXiv:2110.06066] [INSPIRE].
K.J. Costello, Quantizing local holomorphic field theories on twistor space, arXiv:2111.08879 [INSPIRE].
T. Adamo, W. Bu, E. Casali and A. Sharma, Celestial operator products from the worldsheet, JHEP 06 (2022) 052 [arXiv:2111.02279] [INSPIRE].
W. Bu, Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet, Phys. Rev. D 105 (2022) 126029 [arXiv:2111.15584] [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, N.M. Paquette and A. Sharma, Top-Down Holography in an Asymptotically Flat Spacetime, Phys. Rev. Lett. 130 (2023) 061602 [arXiv:2208.14233] [INSPIRE].
S.J. Parke and T.R. Taylor, An Amplitude for n Gluon Scattering, Phys. Rev. Lett. 56 (1986) 2459 [INSPIRE].
V.P. Nair, A Current Algebra for Some Gauge Theory Amplitudes, Phys. Lett. B 214 (1988) 215 [INSPIRE].
Y. Geyer and L. Mason, The SAGEX review on scattering amplitudes Chapter 6: Ambitwistor Strings and Amplitudes from the Worldsheet, J. Phys. A 55 (2022) 443007 [arXiv:2203.13017] [INSPIRE].
D. Skinner, Twistor strings for \( \mathcal{N} \) = 8 supergravity, JHEP 04 (2020) 047 [arXiv:1301.0868] [INSPIRE].
O.T. Engelund and R. Roiban, A twistor string for the ABJ(M) theory, JHEP 06 (2014) 088 [arXiv:1401.6242] [INSPIRE].
N. Berkovits and E. Witten, Conformal supergravity in twistor-string theory, JHEP 08 (2004) 009 [hep-th/0406051] [INSPIRE].
R.A. Reid-Edwards, On Closed Twistor String Theory, arXiv:1212.6047 [INSPIRE].
R. Roiban, M. Spradlin and A. Volovich, On the tree level S matrix of Yang-Mills theory, Phys. Rev. D 70 (2004) 026009 [hep-th/0403190] [INSPIRE].
D. Skinner, A Direct Proof of BCFW Recursion for Twistor-Strings, JHEP 01 (2011) 072 [arXiv:1007.0195] [INSPIRE].
L. Dolan and P. Goddard, Complete Equivalence Between Gluon Tree Amplitudes in Twistor String Theory and in Gauge Theory, JHEP 06 (2012) 030 [arXiv:1111.0950] [INSPIRE].
T. Adamo, Worldsheet factorization for twistor-strings, JHEP 04 (2014) 080 [arXiv:1310.8602] [INSPIRE].
R. Penrose, Solutions of the zero-rest-mass equations, J. Math. Phys. 10 (1969) 38 [INSPIRE].
A. Ferber, Supertwistors and Conformal Supersymmetry, Nucl. Phys. B 132 (1978) 55 [INSPIRE].
M.G. Eastwood, R. Penrose and R.O. Wells, Cohomology and Massless Fields, Commun. Math. Phys. 78 (1981) 305 [INSPIRE].
T. Adamo, E. Casali and S. Nekovar, Yang-Mills theory from the worldsheet, Phys. Rev. D 98 (2018) 086022 [arXiv:1807.09171] [INSPIRE].
T. Adamo, M. Bullimore, L. Mason and D. Skinner, Scattering Amplitudes and Wilson Loops in Twistor Space, J. Phys. A 44 (2011) 454008 [arXiv:1104.2890] [INSPIRE].
S.V. Ketov, Conformal field theory, World Scientific (1995).
P. Francesco, P. Mathieu and D. Senechal, Conformal Field Theory, Graduate Texts in Contemporary Physics, Springer-Verlag (1997).
R. Blumenhagen and E. Plauschinn, Introduction to conformal field theory: with applications to String theory, Lect. Notes Phys. 779 (2009) 1.
T.G. Birthwright, E.W.N. Glover, V.V. Khoze and P. Marquard, Multi-gluon collinear limits from MHV diagrams, JHEP 05 (2005) 013 [hep-ph/0503063] [INSPIRE].
L. Donnay, A. Puhm and A. Strominger, Conformally Soft Photons and Gravitons, JHEP 01 (2019) 184 [arXiv:1810.05219] [INSPIRE].
T. Adamo, L. Mason and A. Sharma, Celestial amplitudes and conformal soft theorems, Class. Quant. Grav. 36 (2019) 205018 [arXiv:1905.09224] [INSPIRE].
L. Ren, A. Schreiber, A. Sharma and D. Wang, to appear (2023).
T. Adamo, L. Mason and A. Sharma, Twistor sigma models for quaternionic geometry and graviton scattering, arXiv:2103.16984 [INSPIRE].
A. Sharma, Twistor sigma models, Ph.D. Thesis, University of Oxford, Oxford U.K. (2022).
W.P. Johnson, The Curious History of Faà di Bruno’s Formula, Am. Math. Mon. 109 (2002) 217.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2211.17124
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Adamo, T., Bu, W., Casali, E. et al. All-order celestial OPE in the MHV sector. J. High Energ. Phys. 2023, 252 (2023). https://doi.org/10.1007/JHEP03(2023)252
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2023)252