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

We study the phase diagram and critical behavior of a two-dimensional lattice SO(Nc) gauge theory (Nc≥3) with two scalar flavors, obtained by partially gauging a maximally O(2Nc) symmetric scalar model. The model is invariant under local SO(Nc) and global O(2) transformations. We show that, for any Nc≥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.