Integrable achiral D5-brane reflections and asymptotic Bethe equations

TL;DR

This paper investigates magnon reflections from a D5-brane within the AdS/CFT framework, demonstrating achiral reflection matrices, their compliance with boundary Yang-Baxter equations, and deriving Bethe equations for different brane orientations.

Contribution

It provides a detailed analysis of D5-brane magnon reflections, establishing achiral reflection matrices and deriving Bethe equations for both vertical and horizontal orientations.

Findings

Reflections are achiral and satisfy boundary Yang-Baxter equations.

Horizontal orientation reflection matrices relate to bulk S-matrices.

Bethe equations are derived for vertical orientation and match closed string forms.

Abstract

We study the reflection of magnons from a D5-brane in the framework of the AdS/CFT correspondence. We consider two possible orientations of the D5-brane with respect to the reference vacuum state, namely vacuum states aligned along "vertical" and "horizontal" directions. We show that the reflections are of the achiral type. We also show that the reflection matrices satisfy the boundary Yang-Baxter equations for both orientations. In the horizontal case the reflection matrix can be interpreted in terms of a bulk S-matrix, S(p, -p), and factorizability of boundary scattering therefore follows from that of bulk scattering. Finally, we solve the nested coordinate Bethe ansatz for the system in the vertical case to find the Bethe equations. In the horizontal case, the Bethe equations are of the same form as those for the closed string.