One-loop Superstring Amplitude From Integrals on Pure Spinors Space

TL;DR

This paper computes the overall constant factor of the one-loop 4-point amplitude for massless NS-NS bosons in Type II superstring theory using the pure spinor formalism, confirming previous results and ensuring consistency with unitarity and S-duality.

Contribution

It introduces a method to evaluate integrals on pure spinor space in the non-minimal formalism, successfully computing the amplitude's constant factor.

Findings

The computed constant matches previous results.

The method confirms the validity of the pure spinor formalism for amplitude calculations.

Ensures consistency with unitarity and S-duality conditions.

Abstract

In the Type II superstring the 4-point function for massless NS-NS bosons at one-loop is well known [1][14]. The overall constant factor in this amplitude is very important because it needs to satisfy the unitarity and S-duality conditions [14]. This coefficient has not been computed in the pure spinor formalism due to the difficulty to solve the integrals on the pure spinors space. In this paper we compute it by using the non-minimal pure spinor formalism and we will show that the answer is in perfect agreement with the one given in [14].