Non perturbative Adler-Bardeen Theorem

TL;DR

This paper proves a nonperturbative version of the Adler-Bardeen theorem in two dimensions using advanced Grassmann integration techniques, extending the theorem beyond perturbation theory.

Contribution

The paper introduces a nonperturbative proof of the Adler-Bardeen theorem in two dimensions, overcoming limitations of perturbative approaches.

Findings

Established a nonperturbative Adler-Bardeen theorem in 2D

Applied Grassmann integration techniques to quantum field theory

Extended the validity of the theorem beyond perturbation series

Abstract

The Adler-Bardeen theorem has been proved only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in $d=2$ by using recently developed technical tools in the theory of Grassmann integration.