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

TL;DR

This paper explores a class of models with massless fermions coupled to boundary rotors, revealing a discrete set of coupling matrices, a connection to monopole-fermion dynamics, and issues with nonunitary scattering matrices.

Contribution

It generalizes monopole-fermion systems by introducing a boundary coupling framework with exact solutions and identifies conditions for coupling matrices, highlighting nonunitarity in the S-matrix.

Findings

Exact partition function and Green's functions derived.

Coupling matrix must satisfy a rationality constraint.

Nonunitary S-matrix observed, with potential unitarity restoration methods.

Abstract

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.