Three-dimensional phase transitions in multiflavor lattice scalar SO(N_{c}) gauge theories

We investigate the phase diagram and finite-temperature transitions of three-dimensional scalar SO(N_{c}) gauge theories with N_{f}≥2 scalar flavors. These models are constructed starting from a maximally O(N)-symmetric multicomponent scalar model (N=N_{c}N_{f}), whose symmetry is partially gauged to obtain an SO(N_{c}) gauge theory, with O(N_{f}) or U(N_{f}) global symmetry for N_{c}≥3 or N_{c}=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(N_{c}) gauge theory. The LGW approach predicts that the transition is of first order for N_{f}≥3. For N_{f}=2 the transition is predicted to be continuous: It belongs to the O(3) vector universality class for N_{c}=2 and to the XY universality class for any N_{c}≥3. We perform numerical simulations for N_{c}=3 and N_{f}=2,3. The numerical results are in agreement with the LGW predictions.