Celestial String Integrands & their Expansions

TL;DR

This paper develops a method to transform one-loop and tree-level open superstring gluon amplitudes into celestial correlators, revealing their structure through Mellin transforms and worldsheet integrals, and analyzing their pole structures.

Contribution

It introduces a novel approach combining Mellin transforms and worldsheet integrals to analyze celestial string integrands at loop and tree levels, providing explicit solutions for specific conformal dimensions.

Findings

Celestial string integrands depend on a simple overall factor of '^{eta-3} at loop level.

The pole structure in the -plane is captured through a fully integrated expression.

Results are consistent with previous '-expansion analyses.

Abstract

We transform the one-loop four-point type $\mathrm{I}$ open superstring gluon amplitude to correlation functions on the celestial sphere including both the (non-)orientable planar and non-planar sector. This requires a Mellin transform with respect to the energies of the scattered strings, as well as to integrate over the open-string worldsheet moduli space. After accomplishing the former we obtain celestial string integrands with remaining worldsheet integrals $\Psi\left(\beta\right)$, where $\beta$ is related to the conformal scaling dimensions of the conformal primary operators under consideration. Employing an alternative approach of performing an $\alpha'$-expansion of the open superstring amplitude first and Mellin transforming afterwards, we obtain a fully integrated expression, capturing the pole structure in the $\beta$-plane. The same analysis is performed at tree-level yielding similar results. We conclude by solving $\Psi\left(\beta\right)$ for specific values of $\beta$, consistently reproducing the results of the $\alpha'$-expansion ansatz. In all approaches we find that the dependence on $\alpha'$ reduces to that of a simple overall factor of $\left(\alpha'\right)^{\beta-3}$ at loop and $\left(\alpha'\right)^{\beta}$ at tree level, consistent with previous literature.