Integrable model of boundary interaction: The paperclip

We consider a model of 2D quantum field theory on a disk, whose bulk dynamics is that of a two-component free massless Bose field X=(X,Y), and interaction occurs at the boundary, where the boundary values (X_B,Y_B) are constrained to special curve-the "paperclip brane". The interaction breaks conformal invariance, but we argue that it preserves integrability. We propose exact expression for the disk partition function (and more general overlap amplitudes 〈P B〉 of the boundary state with all primary states) in terms of solutions of certain ordinary linear differential equations.