Berezinskii-Kosterlitz-Thouless transitions in two-dimensional lattice SO($N_c$) gauge theories with two scalar flavors

TL;DR

This paper investigates Berezinskii-Kosterlitz-Thouless (BKT) phase transitions in two-dimensional lattice SO(Nc) gauge theories with two scalar flavors, revealing universal critical behavior and algebraic correlations.

Contribution

It demonstrates that SO(Nc) gauge theories with two scalars exhibit BKT transitions, extending understanding of phase transitions in gauge theories with continuous symmetries.

Findings

Existence of BKT transitions for all Nc ≥ 3

Identification of algebraic decay of correlations in the low-temperature phase

Finite-size scaling analysis confirms critical properties

Abstract

We study the phase diagram and critical behavior of a two-dimensional lattice SO($N_c$) gauge theory ($N_c \ge 3$) with two scalar flavors, obtained by partially gauging a maximally O($2N_c$) symmetric scalar model. The model is invariant under local SO($N_c$) and global O(2) transformations. We show that, for any $N_c \ge 3$, it undergoes finite-temperature Berezinskii-Kosterlitz-Thouless (BKT) transitions, associated with the global Abelian O(2) symmetry. The transition separates a high-temperature disordered phase from a low-temperature spin-wave phase where correlations decay algebraically (quasi-long range order). The critical properties at the finite-temperature BKT transition and in the low-temperature spin-wave phase are determined by means of a finite-size scaling analysis of Monte Carlo data.