Exact Asymptotic Behaviour of Fermion Correlation Functions in the Massive Thirring Model

TL;DR

This paper derives an exact asymptotic expression for fermion correlation functions in the massive Thirring model, confirming the irrelevance of the mass term at a specific coupling, using Coulomb gas representation.

Contribution

It provides the first exact asymptotic analysis of fermion correlators in the massive Thirring model at a special coupling, linking massive and massless theories.

Findings

Correlation functions match massless theory at 1 8b1b8b1b8 coupling

Mass term is irrelevant at 1 8b1b8 coupling

Exact asymptotic expressions derived using Coulomb gas representation

Abstract

We obtain an exact asymptotic expression for the two-point fermion correlation functions in the massive Thirring model (MTM) and show that, for $\beta^2=8\pi$, they reproduce the exactly known corresponding functions of the massless theory, explicitly confirming the irrelevance of the mass term at this point. This result is obtained by using the Coulomb gas representation of the fermionic MTM correlators in the bipolar coordinate system.