Comments on the Boundary Scattering Phase

TL;DR

This paper proposes solutions to crossing equations for boundary reflection matrices in open string theories, constraining boundary dressing factors and considering residual symmetries, advancing understanding of boundary effects in integrable models.

Contribution

It introduces a simple solution to the crossing equation for boundary reflection matrices with specific residual symmetries and proposes an analogous crossing equation for boundary dressing factors with additional boundary degrees of freedom.

Findings

Derived a solution for the crossing equation with SU(1|2)^2 symmetry.

Proposed an analogous crossing equation for SU(2|2)^2 symmetry.

Constrained the form of boundary dressing factors based on residual symmetries.

Abstract

We present a simple solution to the crossing equation for an open string worldsheet reflection matrix, with boundaries preserving a SU(1|2)^2 residual symmetry, which constrains the boundary dressing factor. In addition, we also propose an analogous crossing equation for the dressing factor where extra boundary degrees of freedom preserve a SU(2|2)^2 residual symmetry.