Fermions Coupled to a Conformal Boundary: A Generalization of the Monopole-Fermion System

We study a class of models in which $N$ flavors of massless fermions on the half line are coupled by an arbitrary orthogonal matrix to $N$ rotors living on the boundary. Integrating out the rotors, we find the exact partition function and Green's functions. We demonstrate that the coupling matrix must satisfy a certain rationality constraint, so there is an infinite, discrete set of possible coupling matrices. For one particular choice of the coupling matrix, this model reproduces the low-energy dynamics of fermions scattering from a magnetic monopole. A quick survey of the Green's functions shows that the S-matrix is nonunitary. This nonunitarity is present in previous results for the monopole-fermion system, although it appears not to have been noted. We indicate how unitarity may be restored by expanding the Fock space to include new states that are unavoidably introduced by the boundary interaction.