Equivalence of Two-Loop Superstring Amplitudes in the Pure Spinor and RNS Formalisms

TL;DR

This paper demonstrates that the two-loop superstring amplitude for four Neveu-Schwarz external states computed using the pure spinor formalism matches the result obtained from the RNS formalism, confirming their equivalence.

Contribution

It proves the equivalence of two-loop four-point superstring amplitudes between pure spinor and RNS formalisms for Neveu-Schwarz states.

Findings

Pure spinor and RNS formalisms yield identical two-loop amplitudes for Neveu-Schwarz states.

Confirms the consistency of pure spinor formalism with established RNS results.

Supports the validity of pure spinor approach in superstring amplitude computations.

Abstract

The pure spinor formalism for the superstring has recently been used to compute massless four-point two-loop amplitudes in a manifestly super-Poincare covariant manner. In this paper, we show that when all four external states are Neveu-Schwarz, the two-loop amplitude coincides with the RNS result.