Lattice-continuum relations for 3d SU ( N) +Higgs theories

Three-dimensional lattice studies have recently attracted a lot of attention, especially in connection with finite-temperature field theories. One ingredient in these studies is a perturbative computation of the 2-loop lattice counterterms, which are exact in the continuum limit. We extend the previous such results to SU( N) gauge thoeries with Higgs fields in the fundamental and adjoint representations. The fundamental SU (3) × SU(2) case might be relevant for the electroweak phase transition in the MSSM, and the adjoint case for the GUT phase transition and for QCD in the high-temperature phase. We also revisit the standard SU(2) × U(1) and U(1) theories.