Notes on parafermionic QFT’s with boundary interaction

The main result of these notes is an analytical expression for the partition function of the circular brane model [1] 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-Schön) model [2] 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 in Ref. [3]. 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 [4].