Anomaly Equations and Intersection Theory

TL;DR

This paper links anomaly cancellation conditions in six-dimensional supergravity to intersection theory identities on Calabi-Yau threefolds, revealing geometric counterparts of anomaly coefficients and advancing understanding of string universality.

Contribution

It demonstrates that anomaly equations can be expressed as three intersection theory identities, identifying geometric counterparts of anomaly coefficients in F-theory compactifications.

Findings

Anomaly equations summarized by three intersection identities

Identification of geometric anomaly coefficient counterparts

Implications for string universality in six dimensions

Abstract

Six-dimensional supergravity theories with N=(1,0) supersymmetry must satisfy anomaly equations. These equations come from demanding the cancellation of gravitational, gauge and mixed anomalies. The anomaly equations have implications for the geometrical data of Calabi-Yau threefolds, since F-theory compactified on an elliptically fibered Calabi-Yau threefold with a section generates a consistent six-dimensional N=(1,0) supergravity theory. In this paper, we show that the anomaly equations can be summarized by three intersection theory identities. In the process we also identify the geometric counterpart of the anomaly coefficients---in particular, those of the abelian gauge groups---that govern the low-energy dynamics of the theory. We discuss the results in the context of investigating string universality in six dimensions.