Notes on parafermionic QFTs with boundary interaction

The main result of these notes is an analytical expression for the partition function of the circular brane model [S.L. Lukyanov, A.B. Zamolodchikov, J. Stat. Mech.: Theor. Exp. (2004) P05003] 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 [V. Ambegaokar, U. Eckern, G. Schön, Phys. Rev. Lett. 48 (1982) 1745] 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 [S.L. Lukyanov, P. Werner, J. Stat. Mech.: Theor. Exp. (2006) P11002]. 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 [P. Fendley, H. Saleur, Phys. Rev. B 60 (1999) 11432].