Correlation functions in a c=1 boundary conformal field theory

TL;DR

This paper derives exact correlation functions in a specific boundary conformal field theory, revealing how boundary interactions influence amplitudes and connecting them to the open-string spectrum.

Contribution

It provides explicit formulas for bulk and boundary correlation functions in a c=1 boundary CFT with a periodic potential, including SU(2) rotation coefficients.

Findings

Exact bulk correlation functions expressed via SU(2) rotations

Boundary amplitudes are independent of boundary interaction

Explicit mixed bulk-boundary correlation functions derived

Abstract

We obtain exact results for correlation functions of primary operators in the two-dimensional conformal field theory of a scalar field interacting with a critical periodic boundary potential. Amplitudes involving arbitrary bulk discrete primary fields are given in terms of SU(2) rotation coefficients while boundary amplitudes involving discrete boundary fields are independent of the boundary interaction. Mixed amplitudes involving both bulk and boundary discrete fields can also be obtained explicitly. Two- and three-point boundary amplitudes involving fields at generic momentum are determined, up to multiplicative constants, by the band spectrum in the open-string sector of the theory.