Some Superstring Amplitude Computations with the Non-Minimal Pure Spinor Formalism

TL;DR

This paper employs the non-minimal pure spinor formalism to compute superstring amplitudes covariantly, revealing how certain tensors naturally arise from pure spinor superspace integrals, thus advancing superstring amplitude calculations.

Contribution

It introduces a covariant method for computing superstring amplitudes using the non-minimal pure spinor formalism, connecting pure spinor integrals with known tensor structures.

Findings

Bosonic contributions match standard results.

Identities show $t_8$ and $\e_{10}$ tensors emerge from pure spinor integrals.

Covariant computation of superstring amplitudes.

Abstract

We use the non-minimal pure spinor formalism to compute in a super-Poincare covariant manner the four-point massless one and two-loop open superstring amplitudes, and the gauge anomaly of the six-point one-loop amplitude. All of these amplitudes are expressed as integrals of ten-dimensional superfields in a "pure spinor superspace" which involves five $\theta$ coordinates covariantly contracted with three pure spinors. The bosonic contribution to these amplitudes agrees with the standard results, and we demonstrate identities which show how the $t_8$ and $\epsilon_{10}$ tensors naturally emerge from integrals over pure spinor superspace.