't Hooft anomalies in metals

TL;DR

This paper reviews how 't Hooft anomalies and emergent symmetries provide a non-perturbative, structural understanding of metallic states, including non-Fermi liquids, without requiring exact solutions.

Contribution

It introduces a framework linking 't Hooft anomalies to metallic properties, offering a novel non-perturbative perspective on strongly coupled metals.

Findings

Metals' properties can be derived from 't Hooft anomalies.

Provides a structural understanding of non-Fermi liquids.

Highlights limitations and open questions in the field.

Abstract

I review some recent results on understanding the physics of metals in an exact non-perturbative way through the powerful field-theoretic concepts of emergent symmetries and 't Hooft anomalies. A 't Hooft anomaly is a discrete topological property that quantum field theories with global symmetries can have. I explain how many of the properties of metals can in fact be viewed as direct consequences of the anomaly. This allows a structural understanding of metals, including non-Fermi liquids, to be obtained even in the absence of any exact solution for the strongly coupled dynamics. I then outline the main limitations and outstanding questions.