Spontaneous Breaking of Parity in 2+1-Dimensional Thirring Model

TL;DR

This paper investigates the vacuum structure of the 2+1-dimensional Thirring model, revealing that parity is spontaneously broken at finite N and that the large N limit may not yield a stable vacuum, challenging previous assumptions.

Contribution

It introduces a new analysis of the vacuum structure using auxiliary fields and demonstrates spontaneous parity breaking at finite N, highlighting issues with the large N approximation.

Findings

Parity is spontaneously broken at finite N

No stable vacuum exists in the large N limit

Detailed analysis for N=2,3 cases provided

Abstract

A new aspect of the vacuum structure of 2+1-dimensional Thirring model is presented. Using the Fierz identity, we split the current-current four-Fermi interaction in terms of a matrix valued auxiliary scalar field and compute its effective potential. Energy consideration shows that contrary to earlier expectations, parity in general is spontaneously broken at any finite order of N, where N is the number of the two component spinors. In the large N limit, there does not exist a stable vacuum of the theory thereby making the application of the large N limit to Thirring model dangerous. A detailed analysis for parity breaking solutions in N=2,3 cases is given.