One-loop superstring six-point amplitudes and anomalies in pure spinor superspace

TL;DR

This paper computes six-point one-loop superstring amplitudes in pure spinor superspace, revealing the origin of gauge anomalies and providing a cohomological framework consistent with S-duality expectations.

Contribution

It introduces a cohomological approach to analyze superstring amplitudes, identifying the role of BRST pseudo-invariants in gauge anomalies within pure spinor formalism.

Findings

Hexagon gauge anomaly linked to BRST pseudo-invariants.

Worldsheet functions are non-singular and total derivatives on moduli space.

Cohomology approach organizes closed-string amplitudes consistent with S-duality.

Abstract

We present the massless six-point one-loop amplitudes in the open and closed superstring using BRST cohomology arguments from the pure spinor formalism. The hexagon gauge anomaly is traced back to a class of kinematic factors in pure spinor superspace which were recently introduced as BRST pseudo-invariants. This complements previous work where BRST invariance arguments were used to derive the non-anomalous part of the amplitude. The associated worldsheet functions are non-singular and demonstrated to yield total derivatives on moduli space upon gauge variation. These cohomology considerations yield an efficient organizing principle for closed-string amplitudes that match expectations from S-duality in the low-energy limit.