Planar Thirring Model in the U(2$N$)-symmetric limit

TL;DR

This paper reviews the 2+1 dimensional Thirring model, exploring potential UV-stable fixed points and phase transitions with spontaneous symmetry breaking, emphasizing non-perturbative lattice simulations with domain wall fermions.

Contribution

It provides a comparative analysis of lattice formulations, especially with domain wall fermions, and predicts a critical flavor number for phase transition.

Findings

Domain wall fermions accurately capture U(2N) symmetry

Predicts critical flavor number 1<N_c<2

Highlights importance of non-perturbative methods

Abstract

I review the Thirring model in 2+1$d$ dimensions, focussing in particular on possible strongly-interacting UV-stable fixed points of the renormalisation group, corresponding to a continuous phase transition where a U($2N$) global symmetry spontaneously breaks to U($N)\otimes$U($N$). Since there is no small parameter in play, a systematic non-perturbative approach such as numerical simulation of lattice field theory is mandated. I compare and contrast various formulations, paying particular attention to models formulated with either staggered or domain wall lattice fermions. Domain wall fermions, which faithfully capture U($2N$) symmetry in the limit of wall separation $L_s\to\infty$, predict a critical flavor number $1<N_c<2$.