Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism

TL;DR

This paper develops a BRST-invariant regularization method for the non-minimal pure spinor formalism, enabling the computation of multiloop superstring amplitudes while maintaining super-Poincare covariance.

Contribution

It introduces a new regularization technique for pure spinor ghosts that simplifies multiloop amplitude calculations in superstring theory.

Findings

Regularization preserves BRST symmetry.

Allows computation of arbitrary multiloop amplitudes.

Simplifies for certain F-term contributions.

Abstract

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRST-invariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the ten-dimensional superspace action which do not involve integration over the maximum number of $\theta$'s.