Towards one-loop SYM amplitudes from the pure spinor BRST cohomology

TL;DR

This paper presents a method to compute one-loop supersymmetric amplitudes in ten-dimensional SYM theory using pure spinor BRST cohomology, revealing structures like BCJ duality and anomalies.

Contribution

It introduces a new approach connecting BRST invariance with cubic-graph organization to derive local, manifestly supersymmetric integrands for one-loop amplitudes.

Findings

Five-point amplitudes satisfy BCJ duality leading to supergravity results.

Six-point amplitudes reveal systematic obstructions to BRST invariance.

Method is applicable to any integrated SYM amplitude in dimensions less than 8.

Abstract

In this paper, we outline a method to compute supersymmetric one-loop integrands in ten-dimensional SYM theory. It relies on the constructive interplay between their cubic-graph organization and BRST invariance of the underlying pure spinor superstring description. The five- and six-point amplitudes are presented in a manifestly local form where the kinematic dependence is furnished by BRST-covariant expressions in pure spinor superspace. At five points, the local kinematic numerators are shown to satisfy the BCJ duality between color and kinematics leading to supergravity amplitudes as a byproduct. At six points, the sources of the hexagon anomaly are identified in superspace as systematic obstructions to BRST invariance. Our results are expected to reproduce any integrated SYM amplitude in dimensions $D< 8$.