  We study a model of 2D QFT with boundary interaction, in which 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, $\theta =0$
and $\theta=\pi$. For $\theta=0$ we propose exact partition function in terms
of solutions of 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 $g_0$ of the tunneling contact. Our proposal
translates to partition function of this model at integer charge.
