Anomalies of QFTs from M-theory and Holography

TL;DR

This paper presents a geometric method to compute 't Hooft anomalies in QFTs derived from M5-branes, utilizing anomaly inflow and holography to connect topological data with field theory anomalies.

Contribution

It introduces a systematic geometric approach to determine anomalies of QFTs from M-theory, including finite N effects, applicable to various dimensions and holographic duals.

Findings

Computed anomalies for multiple 4D and 6D theories from M5-branes.

Demonstrated the method's effectiveness with examples including known M5-brane configurations.

Connected topological data of holographic solutions to field theory anomalies.

Abstract

We describe a systematic way of computing the 't Hooft anomalies for continuous symmetries of Quantum Field Theories in even dimensions that can be geometrically engineered from M5-branes. Our approach is based on anomaly inflow, and characterizes the anomaly polynomial of the QFT in terms of the geometric definition of the field theory. In particular, when the QFT admits a holographic dual, the topological data of the solution is sufficient to compute the anomalies of the dual field theory, including finite terms in $N$. We study several classes of examples in four and six dimensions, with or without known M5-brane probe configurations.