Abstract
Celestial operator product expansions (OPEs) arise from the collinear limit of scattering amplitudes and play a vital role in celestial holography. In this paper, we derive the celestial OPEs of massless fields in string theory from the worldsheet. By studying the worldsheet OPEs of vertex operators in worldsheet CFT and further examining their behaviors in the collinear limit, we find that new vertex operators for the massless fields in string theory are generated and become dominant in the collinear limit. Mellin transforming to the conformal basis yields exactly the celestial OPEs in celestial CFT. We also derive the celestial OPEs from the collinear factorization of string amplitudes and the results derived in these two different methods are in perfect agreement with each other. Our final formulae of celestial OPEs are applicable to general dimensions, corresponding to Einstein-Yang-Mills theory supplemented by some possible higher derivative interactions. Specializing to 4D, we reproduce all the celestial OPEs for gluon and graviton in the literature. We consider various string theories, including the open and closed bosonic string, as well as the closed superstring theory with \( \mathcal{N} \) = 1 and \( \mathcal{N} \) = 2 worldsheet supersymmetry. In the case of \( \mathcal{N} \) = 2 string, we also derive all the \( \overline{\mathrm{SL}\left(2,\mathbb{R}\right)} \) descendant contributions in the celestial OPE; the soft sector of such OPE just yields the w1+∞ algebra after rewriting in terms of chiral modes. Our stringy derivation of celestial OPEs thus initiates the first step towards the microscopic realization of celestial CFT dual to string theory in flat spacetime.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. ’t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [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].
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].
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.-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. Stieberger and T.R. Taylor, Strings on Celestial Sphere, Nucl. Phys. B 935 (2018) 388 [arXiv:1806.05688] [INSPIRE].
T. Adamo, L. Mason and A. Sharma, Celestial amplitudes and conformal soft theorems, Class. Quant. Grav. 36 (2019) 205018 [arXiv:1905.09224] [INSPIRE].
E. Casali and A. Sharma, Celestial double copy from the worldsheet, JHEP 05 (2021) 157 [arXiv:2011.10052] [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, arXiv:2108.08799 [INSPIRE].
S. Banerjee, S. Ghosh and R. Gonzo, BMS symmetry of celestial OPE, JHEP 04 (2020) 130 [arXiv:2002.00975] [INSPIRE].
A. Guevara, Celestial OPE blocks, arXiv:2108.12706 [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].
A. Fotopoulos, S. Stieberger, T.R. Taylor and B. Zhu, Extended Super BMS Algebra of Celestial CFT, JHEP 09 (2020) 198 [arXiv:2007.03785] [INSPIRE].
H. Jiang, Celestial superamplitude in \( \mathcal{N} \) = 4 SYM theory, JHEP 08 (2021) 031 [arXiv:2105.10269] [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].
E. Himwich, M. Pate and K. Singh, Celestial Operator Product Expansions and w1+∞ Symmetry for All Spins, arXiv:2108.07763 [INSPIRE].
T. Adamo, W. Bu, E. Casali and A. Sharma, Celestial OPEs from the worldsheet, talk given at the Workshop on Celestial Amplitudes and Flat Space Holography, Corfu, Greece, 29 August–5 September 2021 and online pdf version at http://www.physics.ntua.gr/corfu2021/ Talks/tim_adamo@gmail_com_01.pdf.
S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96 (2017) 065022 [arXiv:1705.01027] [INSPIRE].
H. Ooguri and C. Vafa, Geometry of N = 2 strings, Nucl. Phys. B 361 (1991) 469 [INSPIRE].
H. Ooguri and C. Vafa, Selfduality and N = 2 String MAGIC, Mod. Phys. Lett. A 5 (1990) 1389 [INSPIRE].
N. Marcus, A Tour through N = 2 strings, in proceedings of the International Workshop on String Theory, Quantum Gravity and the Unification of Fundamental Interactions, Rome, Italy, 21–26 September 1992, hep-th/9211059 [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].
C.P. Boyer and J.F. Plebanski, An infinite hierarchy of conservation laws and nonlinear superposition principles for self-dual Einstein spaces, J. Math. Phys. 26 (1985) 229 [INSPIRE].
D. Kapec and P. Mitra, A d-Dimensional Stress Tensor for Minkd+2 Gravity, JHEP 05 (2018) 186 [arXiv:1711.04371] [INSPIRE].
J. Polchinski, String theory. Volune 2. Superstring theory and beyond, in Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2007).
J. de Boer and S.N. Solodukhin, A Holographic reduction of Minkowski space-time, Nucl. Phys. B 665 (2003) 545 [hep-th/0303006] [INSPIRE].
D. Friedan, S.H. Shenker and E.J. Martinec, Covariant Quantization of Superstrings, Phys. Lett. B 160 (1985) 55 [INSPIRE].
J. Polchinski, String theory. Volume 1. An introduction to the bosonic string, in Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2007).
H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
A. Atanasov, A. Ball, W. Melton, A.-M. Raclariu and A. Strominger, (2, 2) Scattering and the celestial torus, JHEP 07 (2021) 083 [arXiv:2101.09591] [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Quantization of Two-Dimensional Supergravity and Critical Dimensions for String Models, Phys. Lett. B 106 (1981) 63 [INSPIRE].
R. Blumenhagen, D. Lüst and S. Theisen, Basic concepts of string theory, in Theoretical and Mathematical Physics, Springer (2013).
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: 2110.04255
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
Jiang, H. Celestial OPEs and w1+∞ algebra from worldsheet in string theory. J. High Energ. Phys. 2022, 101 (2022). https://doi.org/10.1007/JHEP01(2022)101
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2022)101