Computing the R^4 term at two Superstring Loops

TL;DR

This paper calculates the two-loop contribution to the R^4 term in superstring theory and finds it to be zero, supporting the idea that such terms vanish beyond one loop.

Contribution

It provides an explicit computation confirming the vanishing of the R^4 term at two loops in superstring theory, extending previous theoretical arguments.

Findings

Two-loop R^4 contribution is zero.

Supports the conjecture of no higher-loop R^4 terms.

Validates the integral representation method for amplitude calculations.

Abstract

We use a previously derived integral representation for the four graviton amplitude at two loops in Superstring theory, whose leading term for vanishing momenta gives the two-loop contribution to the R^4 term in the Effective Action. We find by an explicit computation that this contribution is zero, in agreement with a general argument implying the vanishing of the R^4 term beyond one loop.