Ward Identities and chiral anomalies for coupled fermionic chains

TL;DR

This paper derives exact Ward Identities for coupled fermionic chains, revealing chiral anomalies and non-perturbative insights into their thermodynamic properties using Constructive Quantum Field Theory methods.

Contribution

It provides the first exact derivation of Ward Identities and confirms chiral anomalies in coupled fermionic chains, advancing theoretical understanding.

Findings

Existence of chiral anomalies verified

Ward Identities proven non-perturbatively

Implications for thermodynamic properties

Abstract

Coupled fermionic chains are usually described by an effective model written in terms of bonding and anti-bonding spinless fields with linear dispersion in the vicinities of the respective Fermi points. We derive for the first time exact Ward Identities (WI) for this model, proving the existence of chiral anomalies which verify the Adler-Bardeen non-renormalization property. Such WI are expected to play a crucial role in the understanding of the thermodynamic properties of the system. Our results are non-perturbative and are obtained analyzing Grassmann functional integrals by means of Constructive Quantum Field Theory methods.