Thirring Model with Non-conserved Chiral Charge

TL;DR

This paper investigates the Abelian Thirring Model with non-conserved chiral charge, revealing how the Virasoro central charge and conformal dimensions depend on the coupling and chiral charge, and constructing primary fields with arbitrary weights.

Contribution

It introduces a detailed analysis of the Thirring Model with non-conserved chiral charge, including correlation functions and primary field construction, highlighting new dependencies on chiral charge and coupling.

Findings

Virasoro central charge depends on coupling and chiral charge

Conformal dimensions vary with fermionic chiral charge

Constructed primary fields with arbitrary conformal weights

Abstract

We study the Abelian Thirring Model when the fermionic fields have non-conserved chiral charge: $\Delta {\cal Q}_5 =N$. One of the main features we find for this model is the dependence of the Virasoro central charge on both the Thirring coupling constant and $N$. We show how to evaluate correlation functions and in particular we compute the conformal dimensions for fermions and fermionic bilinears, which depend on the fermionic chiral charge. Finally we build primary fields with arbitrary conformal weight.