Exact C=1 Boundary Conformal Field Theories

TL;DR

This paper solves a boundary conformal field theory involving a free scalar field with a periodic boundary interaction, revealing a non-rational CFT with an explicit S-matrix applicable to condensed matter systems.

Contribution

It provides an exact solution for a boundary CFT with a non-trivial S-matrix, expanding the class of exactly solvable models beyond rational theories.

Findings

Explicit S-matrix for boundary scattering at critical period

Identification of a non-rational conformal field theory

Application to condensed matter systems like quantum wires

Abstract

We present a solution of the problem of a free massless scalar field on the half line interacting through a periodic potential on the boundary. For a critical value of the period, this system is a conformal field theory with a non-trivial and explicitly calculable S-matrix for scattering from the boundary. Unlike all other exactly solvable conformal field theories, it is non-rational ({\it i.e.} has infinitely many primary fields). It describes the critical behavior of a number of condensed matter systems, including dissipative quantum mechanics and of barriers in ``quantum wires''.