Free Fermion Representation of a Boundary Conformal Field Theory

TL;DR

This paper demonstrates how a boundary conformal field theory with a boundary interaction can be exactly reformulated using free fermions, revealing hidden symmetries and enabling precise calculations of physical quantities.

Contribution

It provides an exact free fermion representation of a boundary conformal field theory with boundary interactions, uncovering hidden symmetries and calculating the partition function and S-matrix.

Findings

Exact partition function and boundary S-matrix derived.

Spectrum exhibits a band structure interpolating between free and tightly bound states.

Reveals hidden SU(2) symmetry in the boundary conformal field theory.

Abstract

The theory of a massless two-dimensional scalar field with a periodic boundary interaction is considered. At a critical value of the period this system defines a conformal field theory and can be re-expressed in terms of free fermions, which provide a simple realization of a hidden $SU(2)$ symmetry of the original theory. The partition function and the boundary $S$-matrix can be computed exactly as a function of the strength of the boundary interaction. We first consider open strings with one interacting and one Dirichlet boundary, and then with two interacting boundaries. The latter corresponds to motion in a periodic tachyon background, and the spectrum exhibits an interesting band structure which interpolates between free propagation and tight binding as the interaction strength is varied.