Towards Critical Physics in 2+1d with U(2N)-Invariant Fermions

TL;DR

This paper explores lattice formulations of 2+1D fermion theories using domain wall fermions, demonstrating improved convergence and studying phase transitions, symmetry breaking, and spectrum, with implications for critical UV fixed-point physics.

Contribution

It introduces a U(2N)-invariant lattice formulation with domain wall fermions and compares its results to staggered fermions, revealing new insights into symmetry breaking and critical behavior.

Findings

GN model shows symmetry-breaking phase transition and spectrum consistent with large-N.

No symmetry breaking observed in Thirring model up to strong coupling.

Improved convergence to the large-Ls limit with a modified mass term.

Abstract

Interacting theories of N relativistic fermion flavors in reducible spinor representations in 2+1 spacetime dimensions are formulated on a lattice using domain wall fermions (DWF), for which a U(2N) global symmetry is recovered in the limit that the wall separation $L_s$ is made large. The Gross-Neveu (GN) model is studied in the large-N limit and an exponential acceleration of convergence to the large-$L_s$ limit is demonstrated if the usual parity-invariant mass $m\bar\psi\psi$ is replaced by the U(2N)-equivalent $im_3\bar\psi\gamma_3\psi$. The GN model and two lattice variants of the Thirring model are simulated for N = 2 using a hybrid Monte Carlo algorithm, and studies made of the symmetry-breaking bilinear condensate and its associated susceptibility, the axial Ward identity, and the mass spectrum of both fermion and meson excitations. Comparisons are made with existing results obtained using staggered fermions. For the GN model a symmetry-breaking phase transition is observed, the Ward identity is recovered, and the spectrum found to be consistent with large-N expectations. There appears to be no obstruction to the study of critical UV fixed-point physics using DWF. For the Thirring model the Ward identity is not recovered, the spectroscopy measurements are inconclusive, and no symmetry breaking is observed all the way up to the effective strong coupling limit. This is consistent with a critical Thirring flavor number $N_c<2$, contradicting earlier staggered fermion results.