One-loop Superstring Amplitude From Integrals on Pure Spinors Space

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].