Deriving Boundary S Matrices

TL;DR

This paper derives exact boundary S matrices for integrable 1+1D quantum field theories, specifically the sine-Gordon model, using lattice regularization and Bethe ansatz, confirming previous conjectures.

Contribution

It provides an explicit derivation of boundary S matrices for the sine-Gordon model via lattice regularization and Bethe ansatz, validating earlier conjectures.

Findings

Results match Ghoshal and Zamolodchikov's conjectures

Only standard string solutions contribute in the scaling limit

Explicit derivation for sine-Gordon boundary conditions

Abstract

We show how to derive exact boundary $S$ matrices for integrable quantum field theories in 1+1 dimensions using lattice regularization. We do this calculation explicitly for the sine-Gordon model with fixed boundary conditions using the Bethe ansatz for an XXZ-type spin chain in a boundary magnetic field. Our results agree with recent conjectures of Ghoshal and Zamolodchikov, and indicate that the only solutions to the Bethe equations which contribute to the scaling limit are the standard strings.