Abstract
We compute one-loop corrections to the OPE of gluons in the celestial conformal field theory corresponding to Yang-Mills coupled to arbitrary matter. We exploit universal hard/soft factorization to derive an IR finite OPE for the hard gluon operators. This OPE involves logarithms and operators that resemble logarithmic partners of primary operators. We derive an exact all-loop OPE in a limit of the Higgs-regulated planar \( \mathcal{N} \) = 4 super Yang-Mills theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
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.-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].
S. Pasterski, M. Pate and A.-M. Raclariu, Celestial Holography, in 2022 Snowmass Summer Study, (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, arXiv:2203.13022 [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 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].
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. Albayrak, C. Chowdhury and S. Kharel, On loop celestial amplitudes for gauge theory and gravity, Phys. Rev. D 102 (2020) 126020 [arXiv:2007.09338] [INSPIRE].
H.A. González, A. Puhm and F. Rojas, Loop corrections to celestial amplitudes, Phys. Rev. D 102 (2020) 126027 [arXiv:2009.07290] [INSPIRE].
H.A. González and F. Rojas, The structure of IR divergences in celestial gluon amplitudes, JHEP 21 (2021) 171 [arXiv:2104.12979] [INSPIRE].
H. Nastase, F. Rojas and C. Rubio, Celestial IR divergences in general most-subleading-color gluon and gravity amplitudes, JHEP 01 (2022) 136 [arXiv:2111.06861] [INSPIRE].
L.F. Alday, J.M. Henn, J. Plefka and T. Schuster, Scattering into the fifth dimension of N = 4 super Yang-Mills, JHEP 01 (2010) 077 [arXiv:0908.0684] [INSPIRE].
J.M. Henn, S.G. Naculich, H.J. Schnitzer and M. Spradlin, Higgs-regularized three-loop four-gluon amplitude in N = 4 SYM: exponentiation and Regge limits, JHEP 04 (2010) 038 [arXiv:1001.1358] [INSPIRE].
J.M. Henn, S.G. Naculich, H.J. Schnitzer and M. Spradlin, More loops and legs in Higgs-regulated N = 4 SYM amplitudes, JHEP 08 (2010) 002 [arXiv:1004.5381] [INSPIRE].
Z. Bern, L.J. Dixon and V.A. Smirnov, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev. D 72 (2005) 085001 [hep-th/0505205] [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].
M.L. Mangano, S.J. Parke and Z. Xu, Duality and Multi-Gluon Scattering, Nucl. Phys. B 298 (1988) 653 [INSPIRE].
F.A. Berends and W.T. Giele, Recursive Calculations for Processes with n Gluons, Nucl. Phys. B 306 (1988) 759 [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 and D.A. Kosower, Progress in one loop QCD computations, Ann. Rev. Nucl. Part. Sci. 46 (1996) 109 [hep-ph/9602280] [INSPIRE].
Z. Bern and G. Chalmers, Factorization in one loop gauge theory, Nucl. Phys. B 447 (1995) 465 [hep-ph/9503236] [INSPIRE].
M.L. Mangano and S.J. Parke, Multiparton amplitudes in gauge theories, Phys. Rept. 200 (1991) 301 [hep-th/0509223] [INSPIRE].
L.J. Dixon, Calculating scattering amplitudes efficiently, in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 95): QCD and Beyond, (1996), pp. 539–584 [hep-ph/9601359] [INSPIRE].
Z. Bern, V. Del Duca, W.B. Kilgore and C.R. Schmidt, The infrared behavior of one loop QCD amplitudes at next-to-next-to leading order, Phys. Rev. D 60 (1999) 116001 [hep-ph/9903516] [INSPIRE].
D.A. Kosower and P. Uwer, One loop splitting amplitudes in gauge theory, Nucl. Phys. B 563 (1999) 477 [hep-ph/9903515] [INSPIRE].
D.A. Kosower, All order collinear behavior in gauge theories, Nucl. Phys. B 552 (1999) 319 [hep-ph/9901201] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, Two-loop g → gg splitting amplitudes in QCD, JHEP 08 (2004) 012 [hep-ph/0404293] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, One loop corrections to two quark three gluon amplitudes, Nucl. Phys. B 437 (1995) 259 [hep-ph/9409393] [INSPIRE].
A. Sen, Asymptotic Behavior of the Wide Angle On-Shell Quark Scattering Amplitudes in Nonabelian Gauge Theories, Phys. Rev. D 28 (1983) 860 [INSPIRE].
L.J. Dixon, L. Magnea and G.F. Sterman, Universal structure of subleading infrared poles in gauge theory amplitudes, JHEP 08 (2008) 022 [arXiv:0805.3515] [INSPIRE].
E. Gardi and L. Magnea, Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes, JHEP 03 (2009) 079 [arXiv:0901.1091] [INSPIRE].
E. Gardi and L. Magnea, Infrared singularities in QCD amplitudes, Nuovo Cim. C 32N5-6 (2009) 137 [arXiv:0908.3273] [INSPIRE].
T. Becher and M. Neubert, On the Structure of Infrared Singularities of Gauge-Theory Amplitudes, JHEP 06 (2009) 081 [Erratum ibid. 11 (2013) 024] [arXiv:0903.1126] [INSPIRE].
T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett. 102 (2009) 162001 [Erratum ibid. 111 (2013) 199905] [arXiv:0901.0722] [INSPIRE].
I. Feige and M.D. Schwartz, Hard-Soft-Collinear Factorization to All Orders, Phys. Rev. D 90 (2014) 105020 [arXiv:1403.6472] [INSPIRE].
Y. Ma, A Forest Formula to Subtract Infrared Singularities in Amplitudes for Wide-angle Scattering, JHEP 05 (2020) 012 [arXiv:1910.11304] [INSPIRE].
V. Del Duca, G. Falcioni, L. Magnea and L. Vernazza, Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy, JHEP 02 (2015) 029 [arXiv:1409.8330] [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].
N. Kalyanapuram, Soft Gravity by Squaring Soft QED on the Celestial Sphere, Phys. Rev. D 103 (2021) 085016 [arXiv:2011.11412] [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].
L. Magnea, Non-abelian infrared divergences on the celestial sphere, JHEP 05 (2021) 282 [arXiv:2104.10254] [INSPIRE].
I.A. Korchemskaya and G.P. Korchemsky, On lightlike Wilson loops, Phys. Lett. B 287 (1992) 169 [INSPIRE].
L. Magnea and G.F. Sterman, Analytic continuation of the Sudakov form-factor in QCD, Phys. Rev. D 42 (1990) 4222 [INSPIRE].
J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, On planar gluon amplitudes/Wilson loops duality, Nucl. Phys. B 795 (2008) 52 [arXiv:0709.2368] [INSPIRE].
J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes, Nucl. Phys. B 826 (2010) 337 [arXiv:0712.1223] [INSPIRE].
Z. Bern, L.J. Dixon, D.A. Kosower, R. Roiban, M. Spradlin, C. Vergu et al., The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory, Phys. Rev. D 78 (2008) 045007 [arXiv:0803.1465] [INSPIRE].
F. Cachazo, M. Spradlin and A. Volovich, Leading Singularities of the Two-Loop Six-Particle MHV Amplitude, Phys. Rev. D 78 (2008) 105022 [arXiv:0805.4832] [INSPIRE].
D. García-Sepúlveda, A. Guevara, J. Kulp and J. Wu, Notes on resonances and unitarity from celestial amplitudes, JHEP 09 (2022) 245 [arXiv:2205.14633] [INSPIRE].
V. Gurarie, Logarithmic operators in conformal field theory, Nucl. Phys. B 410 (1993) 535 [hep-th/9303160] [INSPIRE].
M. Hogervorst, M. Paulos and A. Vichi, The ABC (in any D) of Logarithmic CFT, JHEP 10 (2017) 201 [arXiv:1605.03959] [INSPIRE].
M. Flohr, Bits and pieces in logarithmic conformal field theory, Int. J. Mod. Phys. A 18 (2003) 4497 [hep-th/0111228] [INSPIRE].
R. Nivesvivat and S. Ribault, Logarithmic CFT at generic central charge: from Liouville theory to the Q-state Potts model, SciPost Phys. 10 (2021) 021 [arXiv:2007.04190] [INSPIRE].
J. Rasmussen, On conformal Jordan cells of finite and infinite rank, Lett. Math. Phys. 73 (2005) 83 [hep-th/0408029] [INSPIRE].
K. Costello and N.M. Paquette, On the associativity of one-loop corrections to the celestial OPE, 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].
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: 2208.14416
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
Bhardwaj, R., Lippstreu, L., Ren, L. et al. Loop-level gluon OPEs in celestial holography. J. High Energ. Phys. 2022, 171 (2022). https://doi.org/10.1007/JHEP11(2022)171
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2022)171