Consistency conditions from generalized-unitarity

TL;DR

This paper reformulates gauge anomaly cancellation conditions using on-shell methods, revealing how locality constraints in the S-matrix relate to anomaly cancellation and the emergence of new particles.

Contribution

It introduces an on-shell perspective on anomaly cancellation, connecting locality issues in the S-matrix to gauge anomalies and spectrum modifications.

Findings

In 4D, anomaly cancellation requires vanishing cubic Casimir.

In 6D, non-vanishing symmetric trace indicates a Green-Schwarz mechanism.

Rational terms can reveal new particles in the spectrum.

Abstract

In the modern on-shell approach, the perturbative S-matrix is constructed iteratively using on-shell building blocks with manifest unitarity. As only gauge invariant quantities enter in the intermediate steps, the notion of gauge anomaly is absent. In this letter, we rephrase the anomaly cancellation conditions in a purely on-shell language. We demonstrate that while the unitarity-methods automatically lead to a unitary S-matrix, the rational terms that are required to enforce locality, invariably give rise to inconsistent factorization channels in chiral theories. In four-dimensions, the absence of such inconsistencies implies the vanishing of the cubic Casimir of the gauge group. In six-dimensions, if the symmetric trace of four generators does not vanish, the rational term develops a factorization channel revealing a new particle in the spectrum: the two-form of the Green-Schwarz mechanism. Thus in the purely on-shell construction, the notion of gauge-anomaly is replaced by the difficulty to consistently impose locality on the unitary S-matrix.