Anomaly Cancelation in Field Theory and F-theory on a Circle

TL;DR

This paper explores how gauge anomalies in higher-dimensional theories manifest after circle compactification, identifying symmetries that ensure anomaly cancellation in lower-dimensional effective theories, with implications for F-theory models.

Contribution

It introduces a set of transformations based on higher-dimensional gauge symmetries that explain anomaly cancellation in compactified theories and F-theory geometries.

Findings

Identifies transformations that encode anomaly cancellation conditions.

Shows that symmetries ensure anomaly cancellation in F-theory models.

Provides a framework connecting higher-dimensional anomalies to lower-dimensional effective theories.

Abstract

We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional Kaluza-Klein theory obtained after circle compactification. We identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the Coulomb branch. The maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced Chern-Simons terms in the three- and five-dimensional effective theory. The arising symmetries are argued to play a key role in the study of the M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact that all fully resolved F-theory geometries inducing multiple Abelian gauge groups or non-Abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure Abelian or pure non-Abelian anomalies in these models.