Fusion of conformal interfaces

We study the fusion of conformal interfaces in the c = 1 conformal field theory. We uncover an elegant structure reminiscent of that of black holes in supersymmetric theories. The role of the BPS black holes is played by topological interfaces, which ( a) minimize the entropy function, ( b) fix through an attractor mechanism one or both of the bulk radii, and ( c) are ( marginally) stable under splitting. One significant difference is that the conserved charges are logarithms of natural numbers, rather than vectors in a charge lattice, as for BPS states. Besides potential applications to condensed-matter physics and number theory, these results point to the existence of large solution-generating algebras in string theory.