# A Modern Point of View on Anomalies

## TL;DR

This paper reviews the concept of anomaly field theory, illustrating how anomalies in d-dimensional theories are encoded in (d+1)-dimensional functors, with applications to supergravity and string theory.

## Contribution

It provides a comprehensive overview of anomaly field theories, including examples, classical recovery, and recent advances in anomaly cancellation in high-dimensional theories.

## Key findings

- Anomaly field theories encode anomalies as (d+1)-dimensional functors.
- Global anomaly cancellation is achieved in 6d supergravity using this framework.
- Status of anomaly cancellation checks in string theory is summarized.

## Abstract

We review the concept of anomaly field theory, namely the fact that the anomalies of a $d$-dimensional field theory can be encoded in a $d+1$-dimensional field theory functor. We give numerous examples of anomaly field theories, explain how classical facts about anomalies are recovered from the anomaly field theory, and review recent work on global anomaly cancellation in 6d supergravity where this concept was instrumental. We also sketch the status of global anomaly cancellation checks in string theory. This paper is based on a talk given at the Durham Symposium `Higher Structures in M-theory' in August 2018.