Exact solution of a massless scalar field with a relevant boundary interaction

TL;DR

This paper provides an exact analytical solution for a massless scalar field with a boundary interaction, revealing the boundary RG flow, scattering properties, and boundary entropy, with implications for quantum Hall systems and dissipative quantum mechanics.

Contribution

It presents the exact S matrix and boundary entropy for the boundary sine-Gordon model in the massless limit, clarifying scattering and RG flow in this boundary field theory.

Findings

Boundary RG flow from Neumann to Dirichlet conditions for ^2 < 8\u03c0

Exact S matrix for particles scattering off the boundary

Calculation of boundary entropy along the RG flow

Abstract

We solve exactly the "boundary sine-Gordon" system of a massless scalar field \phi with a \cos[\beta\phi/2] potential at a boundary. This model has appeared in several contexts, including tunneling between quantum-Hall edge states and in dissipative quantum mechanics. For \beta^2 < 8\pi, this system exhibits a boundary renormalization-group flow from Neumann to Dirichlet boundary conditions. By taking the massless limit of the sine-Gordon model with boundary potential, we find the exact S matrix for particles scattering off the boundary. Using the thermodynamic Bethe ansatz, we calculate the boundary entropy along the entire flow. We show how these particles correspond to wave packets in the classical Klein-Gordon equation, thus giving a more precise explanation of scattering in a massless theory.