Axial anomaly in multi-Weyl and triple-point semimetals

TL;DR

This paper derives the axial anomaly expression in multi-Weyl and triple-point semimetals using three methods, revealing its independence from Lorentz symmetry and dependence on gauge structure, and discusses its stability under parameter changes.

Contribution

It provides a comprehensive derivation of the axial anomaly in complex semimetals without symmetry restrictions, using multiple approaches for validation.

Findings

Anomaly form is independent of Lorentz symmetry.

Anomaly depends on the gauge structure group.

Anomaly coefficient remains stable under smooth modifications.

Abstract

We derive the expression of the abelian axial anomaly in the so-called multi-Weyl and triple-point crossing semimetals. No simplifying restrictions are assumed on the symmetry of the spectrum. Three different computation methods are considered: the perturbative quantum field theory procedure which is based on the evaluation of the one-loop Feynman diagrams, the Nielsen-Ninomiya method, and the Atiyah-Singer index argument. It is shown that the functional form of the axial anomaly does not depend on the Lorentz symmetry, but it is determined by the gauge structure group. We discuss the stability of the anomaly - stemming from the quantisation of the anomaly coefficient - under smooth modifications of the lagrangian parameters.