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,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.