Infinite dimension reflection matrices in the sine-Gordon model with a boundary

TL;DR

This paper introduces an alternative approach to integrable boundary conditions in the sine-Gordon model, emphasizing infinite-dimensional reflection matrices that account for boundary topological charge changes during soliton reflections.

Contribution

It proposes a novel framework involving infinite-dimensional reflection matrices linked to boundary topological charge, expanding the understanding of boundary effects in integrable quantum field theories.

Findings

Infinite-dimensional reflection matrices are more general than traditional two-parameter matrices.

Boundary topological charge influences soliton reflection dynamics.

The approach connects boundary conditions with defect structures in the model.

Abstract

Using the sine-Gordon model as the prime example an alternative approach to integrable boundary conditions for a theory restricted to a half-line is proposed. The main idea is to explore the consequences of taking into account the topological charge residing on the boundary and the fact it changes as solitons in the bulk reflect from the boundary. In this context, reflection matrices are intrinsically infinite dimensional, more general than the two-parameter Ghoshal-Zamolodchikov reflection matrix, and related in an intimate manner with defects.