The phase diagram of three-dimensional SU(3) plus adjoint Higgs theory

We study the phase diagram of the three-dimensional SU(3)+adjoint Higgs theory with lattice Monte Carlo simulations. A critical line consisting of a first order line, a tricritical point and a second order line, divides the phase diagram into two parts distinguished by [Tr A(0)(3)] = 0 and not equal 0. The location and the type of the critical line are determined by measuring the condensates [Tr A(0)(2)] and [Tr A(0)(3)], and the masses of scalar and vector excitations. Although in principle there can be different types of broken phases, corresponding perturbatively to unbroken SU(2) x U(1) or U(1) x U(1) symmetries, we find that dynamically only the broken phase with SU(2) x U(1)-like properties is realized. The relation of the phase diagram to 4d finite temperature QCD is discussed.