  The main result of these notes is an analytical expression for the partition
function of the circular brane model for arbitrary values of the topological
angle. The model has important applications in condensed matter physics. It is
related to the dissipative rotator (Ambegaokar-Eckern-Schon) model and
describes a ``weakly blocked'' quantum dot with an infinite number of tunneling
channels under a finite gate voltage bias. A numerical check of the analytical
solution by means of Monte Carlo simulations has been performed recently. To
derive the main result we study the so-called boundary parafermionic
sine-Gordon model. The latter is of certain interest to condensed matter
applications, namely as a toy model for a point junction in the multichannel
quantum wire.
