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

Abstract

I review the Thirring model in 2+1d 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 )⊗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 → ∞, predict a critical flavor number 1 < N c < 2.