Generalized Thirring Models

TL;DR

This paper provides a comprehensive analysis of generalized Thirring models, exploring their equations of state, effects of boundary conditions, coupling to gravity, and bosonization in curved space-times, with detailed calculations of conformal properties and finite size effects.

Contribution

It introduces new insights into the effects of four-Fermi interactions, boundary conditions, and gravity coupling on the Thirring model, including explicit formulas for partition functions and condensates.

Findings

Modified equations of state due to four-Fermi interactions

Complex fermionic determinants from chemical potentials and boundary conditions

Explicit expressions for partition functions and chiral condensates

Abstract

The Thirring model and various generalizations of it are analyzed in detail. The four-Fermi interaction modifies the equation of state. Chemical potentials and twisted boundary conditions both result in complex fermionic determinants which are analyzed. The non-minimal coupling to gravity does deform the conformal algebra which in particular contains the minimal models. We compute the central charges, conformal weights and finite size effects. For the gauged model we derive the partition functions and the explicit expression for the chiral condensate at finite temperature and curvature. The Bosonization in compact curved space-times is also investigated.