Reflecting magnons from D7 and D5 branes

TL;DR

This paper derives reflection matrices for magnons scattering off D7 and D5 branes in AdS5xS5, using symmetry principles and analyzing their integrability properties at weak and strong coupling.

Contribution

It provides the first derivation of reflection matrices for open strings ending on D7 and D5 branes, including their boundary Yang-Baxter properties and coupling consistency.

Findings

D7 reflection matrices obey the boundary Yang-Baxter Equation in one orientation.

D5 reflection matrices do not satisfy the boundary Yang-Baxter Equation.

Results are consistent with existing weak and strong coupling analyses.

Abstract

We obtain the reflection matrices for the scattering of elementary magnons from certain open boundaries, corresponding to open strings ending on D7 and D5 branes in $AdS_5\times S^5$. In each case we consider two possible orientations for the vacuum state. We show that symmetry arguments are sufficient to determine the reflection matrices up to at most two unknown functions. The D7 reflection matrices obey the boundary Yang Baxter-Equation. This is automatic for one vacuum orientation, and requires a natural choice of ratio between two unknowns for the other. In contrast, the D5 reflection matrices do not obey the boundary Yang Baxter-Equation. In both cases we show consistency with the existent weak and strong coupling results.