# Lattice Gauge Theory of Three Dimensional Thirring Model

## TL;DR

This study uses lattice gauge theory simulations to investigate the three-dimensional Thirring model, revealing spontaneous chiral symmetry breaking for certain fermion flavors and suggesting a critical flavor number where behavior changes.

## Contribution

It provides the first lattice gauge theory simulation evidence for chiral symmetry breaking in the three-dimensional Thirring model with multiple fermion flavors.

## Key findings

- Chiral symmetry is spontaneously broken for N=2, 4, 6.
- Evidence of a critical fermion flavor number N_cr between 2 and 6.
- Finite volume effects are significant but do not obscure the main results.

## Abstract

Three dimensional Thirring model with $N$ four-component Dirac fermions, reformulated as a lattice gauge theory, is studied by computer simulation. According to an $8^{3}$ data and preliminary $16^3$ data, chiral symmetry is found to be spontaneously broken for $N=2,\;4$ and 6. $N=2$ data exhibits long tail of the non-vanishing chiral condensate into weak coupling region, and $N=6$ case shows phase separation between the strong coupling region and the weak coupling region. Although the comparison between $8^3$ data and $16^3$ data shows large finite volume effects, an existence of the critical fermion flavor number $N_{{\rm cr}}$ $(2<N_{{\rm cr}}<6)$ for which the chiral behavior changes its character, is suggested by the current numerical data.