Monopole-Catalysed Baryon Decay: A Boundary Conformal Field Theory Approach

TL;DR

This work reframes the Callan–Rubakov monopole-catalyzed baryon-number violation in terms of boundary conformal field theory, showing that the low-energy limit is governed by conformally invariant boundary conditions on free fermions at the dyon. By employing non-abelian bosonization, Ishibashi states, and Cardy’s boundary-state formalism, the authors construct the dyon boundary state $|D\theta\rangle$ for arbitrary $N$, with the topological angle $\theta$ acting as a boundary parameter that reproduces the correct Green's functions and reproduces Polchinski’s results when integrating out the impurity. For $N\le 2$ the boundary conditions reduce to linear, Fermi-liquid-type relations, while for $N>2$ the boundary conditions are non-Fermi-liquid, yielding fractional scaling and exotic charge-flavour structures; in the even-$N$ case a CP-invariant, non-degenerate ground state exists. The approach provides a unified, impurity-based CFT framework for the Callan–Rubakov effect and connects to boundary problems in quantum wires, with explicit matching of Green's functions and topological-θ dependence.

Abstract

Monopole-mediated baryon number violation, the Callan-Rubakov effect, is reexamined using boundary conformal field theory techniques. It is shown that the low-energy behaviour is described simply by free fermions with a conformally invariant boundary condition at the dyon location. When the number of fermion flavours is greater than two, this boundary condition is of a non-trivial type which has not been elucidated previously.