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

Asymptotic Bethe equations for open boundaries in planar AdS/CFT