Comments on Global Symmetries, Anomalies, and Duality in (2+1)d

TL;DR

This paper investigates the global symmetries and 't Hooft anomalies in (2+1)d quantum field theories, revealing how these anomalies constrain the infrared dynamics and dualities of the theories.

Contribution

It provides a detailed analysis of global symmetries, their anomalies, and the implications for dualities in (2+1)d quantum field theories.

Findings

Identification of subtle global symmetry observables

Discovery of 't Hooft anomalies constraining IR behavior

Constraints on duality conjectures in (2+1)d theories

Abstract

We analyze in detail the global symmetries of various (2+1)d quantum field theories and couple them to classical background gauge fields. A proper identification of the global symmetries allows us to consider all non-trivial bundles of those background fields, thus finding more subtle observables. The global symmetries exhibit interesting 't Hooft anomalies. These allow us to constrain the IR behavior of the theories and provide powerful constraints on conjectured dualities.