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We study a model of 2D QFT with boundary interaction, in which two-componentmassless Bose field is constrained to a circle at the boundary. We argue thatthis model is integrable at two values of the topological angle, $\theta =0$and $\theta=\pi$. For $\theta=0$ we propose exact partition function in termsof solutions of ordinary linear differential equation. The circular brane modelis equivalent to the model of quantum Brownian dynamics commonly used indescribing the Coulomb charging in quantum dots, in the limit of smalldimensionless resistance $g_0$ of the tunneling contact. Our proposaltranslates to partition function of this model at integer charge.Comment: 20 pages, minor change

Integrable circular brane model and Coulomb charging at large conduction