A Modern Point of View on Anomalies

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.

14 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018 v2: References added

References in corpus (4)

• Global aspects of the space of 6D N = 1 supergravities
• Quantization of anomaly coefficients in 6D $\mathcal{N}=(1,0)$ supergravity
• 8d gauge anomalies and the topological Green-Schwarz mechanism
• The global anomalies of (2,0) superconformal field theories in six dimensions

Cited by in corpus (8)

• IIB flux non-commutativity and the global structure of field theories
• The anomaly that was not meant IIB
• Defect $a$-Theorem and $a$-Maximization
• Gapless edge modes in (4+1)-dimensional topologically massive tensor gauge theory and anomaly inflow for subsystem symmetry
• General anomaly matching by Goldstone bosons
• The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
• Anomalies and the Green-Schwarz Mechanism
• Symmetry TFTs from String Theory