Three-dimensional phase transitions in multiflavor lattice scalar SO(Nc) gauge theories

We investigate the phase diagram and finite-temperature transitions of three-dimensional scalar SO(Nc) gauge theories with Nf≥2 scalar flavors. These models are constructed starting from a maximally O(N)-symmetric multicomponent scalar model (N=NcNf), whose symmetry is partially gauged to obtain an SO(Nc) gauge theory, with O(Nf) or U(Nf) global symmetry for Nc≥3 or Nc=2, respectively. These systems undergo finite-temperature transitions, where the global symmetry is broken. Their nature is discussed using the Landau-Ginzburg-Wilson (LGW) approach, based on a gauge-invariant order parameter, and the continuum scalar SO(Nc) gauge theory. The LGW approach predicts that the transition is of first order for Nf≥3. For Nf=2 the transition is predicted to be continuous: It belongs to the O(3) vector universality class for Nc=2 and to the XY universality class for any Nc≥3. We perform numerical simulations for Nc=3 and Nf=2,3. The numerical results are in agreement with the LGW predictions.