Integrable circular brane model and Coulomb charging at large conduction

We study a model of 2D QFT with boundary interaction, in which a two-component massless Bose field is constrained to a circle at the boundary. We argue that this model is integrable at two values of the topological angle,= 0 and For= 0 we propose an exact partition function in terms of solutions of an ordinary linear differential equation. The circular brane model is equivalent to the model of quantum Brownian dynamics commonly used in describing the Coulomb charging in quantum dots, in the limit of small dimensionless resistance g0 of the tunnelling contact. Our proposal translates to a partition function of this model at integer charge.