Multi-loop amplitudes in maximally supersymmetric pure spinor field theory

TL;DR

This paper explores multi-loop amplitudes in maximally supersymmetric field theories using a pure spinor formalism, revealing the necessity of contact terms for BRST invariance and providing proofs for amplitude vanishing conditions.

Contribution

It develops a first quantised pure spinor formalism for field theories with maximal supersymmetry, including ghost fields and contact term analysis.

Findings

BRST invariance requires specific contact terms beyond two loops.

Proof of the no-triangle hypothesis in supersymmetric amplitudes.

Demonstration of vanishing amplitudes with fewer than four external particles.

Abstract

This paper provides a more detailed background to the results of arXiv:1004.2692 concerning properties of multi-loop amplitudes in a pure spinor formulation of field theories with maximal supersymmetry. This involves the development of a first quantised field theory version of the non-minimal pure spinor formalism originally designed for describing superstring amplitudes. In addition to superspace world-line fields, the formalism involves a set of world-line ghost fields that are required for implementing BRST invariance with a composite b ghost. In particular, we show that BRST invariance requires the presence of certain contact terms. For four-point amplitudes, these are important beyond two loops. We also present an alternative proof of the "no-triangle hypothesis" and the vanishing of amplitudes with fewer than four external particles.