Celestial OPEs and $ w_{1+\infty}$ algebra from worldsheet in string theory

TL;DR

This work establishes a concrete bridge between string worldsheet dynamics and celestial holography by deriving celestial OPEs directly from worldsheet OPEs across bosonic and supersymmetric string theories, and corroborating these results with collinear-factorization analyses of string amplitudes. The approach uncovers how new massless vertex operators dominate in the collinear limit and shows that Mellin transformations to the conformal basis reproduce the celestial OPE structure in celestial CFT. The analysis spans open/closed bosonic strings, heterotic and Type I/II superstrings, and extends to N=2 string theory in (2,2) signature, where all overline SL(2, R) descendants emerge and lead to the w_{1+∞} algebra in the soft sector. Together, these results initiate a string-theoretic realization of celestial holography and reveal deep connections between worldsheet CFT, celestial CFT, and infinite-dimensional symmetry algebras. The findings suggest fruitful directions for loop corrections, open-closed fusion mechanisms, and a direct conformal-basis construction of celestial operators within string theory.

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 $\overline{SL (2,\mathbb R)}$ descendant contributions in the celestial OPE; the soft sector of such OPE just yields the $w_{1+\infty}$ algebra after rewriting in terms of chiral modes. Our stringy derivation of celestial OPEs thus initiates the first step towards the realization of celestial holography in string theory.