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Celestial operator product expansions (OPEs) arise from the collinear limitof scattering amplitudes and play a vital role in celestial holography. In thispaper, we derive the celestial OPEs of massless fields in string theory fromthe worldsheet. By studying the worldsheet OPEs of vertex operators inworldsheet CFT and further examining their behaviors in the collinear limit, wefind that new vertex operators for the massless fields in string theory aregenerated and become dominant in the collinear limit. Mellin transforming tothe conformal basis yields exactly the celestial OPEs in celestial CFT. We alsoderive the celestial OPEs from the collinear factorization of string amplitudesand the results derived in these two different methods are in perfect agreementwith each other. Our final formulae of celestial OPEs are applicable to generaldimensions, corresponding to Einstein-Yang-Mills theory supplemented by somepossible higher derivative interactions. Specializing to 4D, we reproduce allthe celestial OPEs for gluon and graviton in the literature. We considervarious string theories, including the open and closed bosonic string, as wellas the closed superstring theory with $\mathcal N=1$ and $\mathcal N=2$worldsheet supersymmetry. In the case of $\mathcal N=2$ string, we also deriveall the $\overline{SL (2,\mathbb R)}$ descendant contributions in the celestialOPE; the soft sector of such OPE just yields the $w_{1+\infty}$ algebra afterrewriting in terms of chiral modes. Our stringy derivation of celestial OPEsthus initiates the first step towards the realization of celestial holographyin string theory.

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