The Bethe Ansatz Equations for Reflecting Magnons

TL;DR

This paper derives Bethe Ansatz equations for reflecting magnons in integrable models with specific symmetries, relevant for understanding open string spectra in AdS/CFT correspondence.

Contribution

It introduces Bethe Ansatz equations for particles with $su(2|2)$ symmetry on a half line with open boundaries, extending integrability methods to new boundary conditions.

Findings

Derived Bethe Ansatz equations for $su(2|2)$ invariant systems with open boundaries.

Connected the equations to the spectrum of open strings on $AdS_5 imes S^5$ with giant graviton branes.

Formulated a related one-dimensional spin chain Hamiltonian.

Abstract

We derive the Bethe Ansatz Equations on the half line for particles interacting through factorized $S$-matrices invariant relative to the centrally extended $su(2|2)$ Lie superalgebra and $su(1|2)$ open boundaries. These equations may be of relevance for the study of the spectrum of open strings on $AdS_{5} \times S^5$ background attached to Y=0 giant graviton branes. An one-dimensional spin chain hamiltonian associated to this system is also derived.