Asymptotic Bethe equations for open boundaries in planar AdS/CFT

TL;DR

This paper derives all-loop Bethe equations for open strings in AdS/CFT with boundaries, providing a detailed spectral analysis for strings ending on giant gravitons and D7-branes, relevant for understanding gauge/string duality with boundaries.

Contribution

It introduces the nested coordinate Bethe ansatz solution for open-boundary scattering in AdS/CFT, extending integrability techniques to boundary conditions and specific D-brane configurations.

Findings

Derived all-loop Bethe equations for open strings with boundaries.

Provided spectral equations for strings ending on giant gravitons.

Extended integrability methods to D7-brane boundary conditions.

Abstract

We solve, by means of a nested coordinate Bethe ansatz, the open-boundaries scattering theory describing the excitations of a free open string propagating in $AdS_5\times S^5$, carrying large angular momentum $J=J_{56}$, and ending on a maximal giant graviton whose angular momentum is in the same plane. We thus obtain the all-loop Bethe equations describing the spectrum, for $J$ finite but large, of the energies of such strings, or equivalently, on the gauge side of the AdS/CFT correspondence, the anomalous dimensions of certain operators built using the epsilon tensor of SU(N). We also give the Bethe equations for strings ending on a probe D7-brane, corresponding to meson-like operators in an $\mathcal N=2$ gauge theory with fundamental matter.