Exact Solution of a Boundary Conformal Field Theory

TL;DR

This paper provides an exact analysis of a boundary conformal field theory involving a free scalar field with boundary interactions, revealing how the boundary state interpolates between different boundary conditions and computing the full scattering matrix.

Contribution

It introduces an exact solution for a boundary CFT with a periodic boundary potential, including the explicit boundary state and scattering matrix, and discusses unitarity via a hidden soliton degree of freedom.

Findings

Boundary state interpolates between Neumann and Dirichlet conditions.

Explicit full S-matrix with particle production is computed.

Unitarity requires a hidden soliton degree of freedom.

Abstract

We study the conformal field theory of a free massless scalar field living on the half line with interactions introduced via a periodic potential at the boundary. An SU(2) current algebra underlies this system and the interacting boundary state is given by a global SU(2) rotation of the left-moving fields in the zero-potential (Neumann) boundary state. As the potential strength varies from zero to infinity, the boundary state interpolates between the Neumann and the Dirichlet values. The full S-matrix for scattering from the boundary, with arbitrary particle production, is explicitly computed. To maintain unitarity, it is necessary to attribute a hidden discrete ``soliton'' degree of freedom to the boundary. The same unitarity puzzle occurs in the Kondo problem, and we anticipate a similar solution.