Superstring loop amplitudes from the field theory limit

TL;DR

This paper introduces a new method to derive superstring loop amplitudes from supergravity integrands using the field theory limit, scattering equations, and modular invariance, successfully reproducing known results at two loops.

Contribution

It presents a novel procedure to obtain superstring loop integrands from supergravity, extending to higher loops and providing a conjecture at three loops.

Findings

Reproduced the two-loop four-point amplitude for superstrings.

Proposed a conjecture for three-loop superstring amplitudes.

Connected supergravity and superstring amplitudes via scattering equations.

Abstract

We propose a procedure to determine the moduli-space integrands of loop-level superstring amplitudes for massless external states in terms of the field theory limit. We focus on the type II superstring. The procedure is to: (i) take a supergravity loop integrand written in a BCJ double-copy representation, (ii) use the loop-level scattering equations to translate that integrand into the ambitwistor string moduli-space integrand, localised on the nodal Riemann sphere, and (iii) uplift that formula to one on the higher-genus surface valid for the superstring, guided by modular invariance. We show how this works for the four-point amplitude at two loops, where we reproduce the known answer, and at three loops, where we present a conjecture that is consistent with a previous proposal for the chiral measure. Useful supergravity results are currently known up to five loops.