Reflecting magnons

TL;DR

This paper investigates the reflection properties of magnons on open strings attached to D-branes in AdS5×S5, deriving boundary reflection matrices and phases, and confirming integrability at weak and strong coupling regimes.

Contribution

It provides the first computation of boundary reflection matrices for open strings on giant gravitons, including phase factors at weak and strong coupling, confirming integrability.

Findings

Boundary reflection matrices obey the boundary Yang-Baxter equation.

A crossing equation for the phase factor is derived.

Results are consistent with integrability at weak and strong coupling.

Abstract

We study the worldsheet reflection matrix of a string attached to a D-brane in $AdS_5 \times S^5$. The D-brane corresponds to a maximal giant graviton and it wraps an $S^3$ inside $S^5$. In the gauge theory, the open string is described by a spin chain with boundaries. We study an open string with a large SO(6) charge, which allows us to focus on one boundary at a time and to define an asymptotic boundary reflection matrix. We consider two cases corresponding to two possible relative orientations for the charges of the giant graviton and the open string. Using the symmetries of the problem we compute the boundary reflection matrix up to a phase. These matrices obey the boundary Yang Baxter equation. A crossing equation is derived for the overall phase. We perform weak coupling computations up to two loops and obtain results that are consistent with integrability. Finally, we determine the phase factor at strong coupling using classical solutions.