Quantum Field Theory and its Anomalies for Topological Matter

TL;DR

This paper explores the role of quantum field theory anomalies, especially chiral and conformal anomalies, in topological materials like insulators and semimetals, linking fundamental physics with observable exotic phenomena.

Contribution

It highlights the connection between quantum field theory anomalies and topological matter, illustrating how these anomalies explain exotic edge currents and response functions in such materials.

Findings

Anomalies underpin resilient edge currents in topological insulators.

Conformal anomalies influence response functions under stress.

Effective actions describe long-range topological interactions.

Abstract

Topology enters in quantum field theory (qft) in multiple forms: one of the most important, in non-abelian gauge theories, being in the identification of the $\theta$ vacuum in QCD. A very relevant aspect of this connection is through the phenomenon of chiral and conformal qft anomalies. It has been realized that a class of materials, comprising topological insulators and Weyl semimetals, also exhibit the phenomenon of anomalies, which are responsible for several exotic phenomena, such as the presence of edge currents, resilient under perturbations and scattering by impurities. Another example comes from the response functions of these materials under thermal and mechanical stresses, that may be performed using correlation functions of stress energy tensors in General Relativity. In this case the conformal anomaly plays an important role. We briefly illustrate some salient features of this correspondence, and the effective action describing the long-range interactions that may account for such topological effects.