Anomaly-Free Supergravities in Six Dimensions

TL;DR

This thesis analyzes anomaly cancellation in six-dimensional N=2 supergravities, identifying solutions for gauge groups and matter content, and explores implications for compactifications and higher-dimensional theories.

Contribution

It provides a comprehensive classification of anomaly-free six-dimensional supergravity models under specific restrictions, advancing understanding of consistent supergravity theories.

Findings

Numerous solutions for ungauged theories satisfying anomaly cancellation.

Few solutions exist for gauged theories with specific restrictions.

Insights into anomaly cancellation in higher-dimensional compactifications.

Abstract

This thesis reviews minimal N=2 chiral supergravities coupled to matter in six dimensions with emphasis on anomaly cancellation. In general, six-dimensional chiral supergravities suffer from gravitational, gauge and mixed anomalies which render the theories inconsistent at the quantum level. Consistency is restored if the anomalies of the theory cancel via the Green-Schwarz mechanism or generalizations thereof. The anomaly cancellation conditions translate into a certain set of constraints for the gauge group of the theory as well as on its matter content. For the case of ungauged theories these constraints admit numerous solutions but, in the case of gauged theories, the allowed solutions are remarkably few. In this thesis, we examine these anomaly cancellation conditions in detail and we present all solutions to these conditions under certain restrictions on the allowed gauge groups and representations, imposed for practical reasons. We also briefly examine anomaly cancellation in the context of Horava-Witten-type compactifications of minimal seven-dimensional supergravity. Finally, we discuss some basic aspects of 4D compactifications of the gauged models.