On the geometrical interpretation of locality in anomaly cancellation

TL;DR

This paper provides a geometric framework for understanding locality in anomaly cancellation, linking local counterterms to intrinsic geometry and expressing global anomaly conditions via equivariant holonomy.

Contribution

It introduces a geometric interpretation of local counterterms and formulates global anomaly cancellation conditions using equivariant holonomy of the Bismut-Freed connection.

Findings

Necessary and sufficient conditions for anomaly cancellation with locality

Intrinsic geometric interpretation of local counterterms

Global anomaly conditions via equivariant holonomy

Abstract

A notion of local section of the determinant line bundle is defined giving necessary and suficient conditions for anomaly cancellation compatible with locality. This definition gives an intrinsic geometrical interpretation of the local counterterms allowed in the renormalization program of quantum field theory. For global anomalies the conditions for anomaly cancellation are expressed in terms of the equivariant holonomy of the Bismut-Freed connection.