Phase structure and nonperturbative states in a three-dimensional adjoint Higgs model

The thermodynamics of a three-dimensional (3D) adjoint Higgs model is considered. We study the properties of the Polyakov loop correlators and the critical behavior at the deconfinement phase transition; Our main tool is a reduction to the 2D sine-Gordon model. The Polyakov loops appear to be connected with the soliton operators in it. The known exact results in the sine-Gordon theory allow us to study in detail the temperature dependence of the string tension; as well as to get some information about the nonperturbative dynamics in the confinement phase. We also consider symmetry restoration at high temperature which makes it possible to construct the phase diagram of the model completely.