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.

Highlights

  • The quest for quantum gravity is one of the most fundamental questions in theoretical physics

  • By studying the worldsheet operator product expansions (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

  • In this paper we provide an approach to deriving celestial OPEs from the worldsheet in string theory

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Summary

Introduction

The quest for quantum gravity is one of the most fundamental questions in theoretical physics. The celestial amplitudes are defined as the Mellin transformation of momentum space scattering amplitude and can be regarded as the correlation functions of celestial operators O∆1(x1)O∆2(x2) · · · in some putative CCFT on the celestial sphere living at boundary null infinity [5, 24] This is very similar to the scattering amplitudes in string theory which are computed by the correlator of vertex operators in worldsheet CFT. In appendix B, we will derive the celestial OPE between gluon and graviton in the open-closed string setup from both the worldsheet perspective and the amplitude approach. The polarizations are denoted as ζ, ξ, e, ε, while always refers to infinitesimal quantity

Preliminary
Kinematics in general dimension
D δabΠμν
Open string vertex operator
Closed string vertex operator
CFT on the worldsheet and on the celestial sphere
Celestial OPE from worldsheet OPE in bosonic string
OPE in open string
General structure of worldsheet OPE
Celestial OPE from worldsheet OPE in superstring
Vertex operator in heterotic string
Celestial OPE from heterotic worldsheet
Celestial OPE from collinear factorization
Celestial OPE for gluon
Celestial OPE in four dimensions
Descendant in OPE from momentum conservation
Conclusion and outlook
OPE in open bosonic string
OPE in closed bosonic string
OPE in heterotic string
B OPE and amplitude in open-closed string theory
Full Text
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