Chiral anomalies on a circle and their cancellation in F-theory

TL;DR

This paper investigates how four-dimensional anomalies manifest and are canceled when theories are compactified on a circle, revealing that anomaly cancellation persists through the appearance of field-dependent Chern-Simons terms and extending the analysis to F-theory models.

Contribution

It provides a detailed analysis of anomaly behavior under circle compactification and demonstrates automatic anomaly cancellation in F-theory via a limit of M-theory on Calabi-Yau fourfolds.

Findings

Anomalies manifest as field-dependent Chern-Simons terms in 3D.

Anomaly cancellation in 4D is preserved upon circle compactification.

F-theory compactifications automatically cancel local anomalies.

Abstract

We study in detail how four-dimensional local anomalies manifest themselves when the theory is compactified on a circle. By integrating out the Kaluza-Klein modes in a way that preserves the four-dimensional symmetries in the UV, we show that the three-dimensional theory contains field-dependent Chern-Simons terms that appear at one-loop. These vanish if and only if the four-dimensional anomaly is canceled, so the anomaly is not lost upon compactification. We extend this analysis to situations where anomalies are canceled through a Green-Schwarz mechanism. We then use these results to show automatic cancellation of local anomalies in F-theory compactifications that can be obtained as a limit of M-theory on a smooth Calabi-Yau fourfold with background flux.