Celestial open strings at one-loop

TL;DR

This paper investigates one-loop celestial amplitudes in open string theory, demonstrating how the Mellin transform relates string and field theory amplitudes on the celestial sphere, and clarifies the role of the string parameter ' in the loop expansion.

Contribution

It shows that the Mellin transform commutes with the field theory limit in string theory, connecting one-loop celestial amplitudes to the worldline formalism and clarifying the ' dependence.

Findings

Mellin transform reproduces celestial one-loop field theory amplitudes.

The ' dependence remains a simple overall factor with a shifted power at one-loop.

The loop expansion is organized by the dimensionless parameter g_{10}^2/'^3.

Abstract

We study celestial amplitudes in string theory at one-loop. Celestial amplitudes describe scattering processes of boost eigenstates and relate to amplitudes in the more standard basis of momentum eigenstates through a Mellin transform. They are thus sensitive to both the ultraviolet and the infrared, which raises the question of how to appropriately take the field theory limit of string amplitudes in the celestial basis. We address this problem in the context of four-dimensional genus-one scattering processes of gluons in open string theory which reach the two-dimensional celestial sphere at null infinity. We show that the Mellin transform commutes with the adequate limit in the worldsheet moduli space and reproduces the celestial one-loop field theory amplitude expressed in the worldline formalism. The dependence on $\alpha'$ continues to be a simple overall factor in one-loop celestial amplitudes albeit with a power that is shifted by three units with respect to tree-level, thus making manifest that the dimensionless parameter $g_{10}^2/\alpha'^3$ organizes the loop expansion in the celestial basis.