Find in Library

Abstract The problem of separation of variables (SoV) in supersymmetric spin chains is closely related to the calculation of correlation functions in N=4 $$ \mathcal{N}=4 $$ SYM theory which is integrable in the planar limit. To address this question we find a compact formula for the spin chain eigenstates, which does not have any sums over auxiliary roots one usually gets in the widely adopted nested Bethe ansatz. Our construction only involves one application of a simple B g (u k ) operator to the reference state for each of the magnons, in complete analogy with the su2 $$ \mathfrak{s}\mathfrak{u}(2) $$ algebraic Bethe ansatz. This generalizes our SoV based construction for sun $$ \mathfrak{s}\mathfrak{u}(n) $$ to the supersymmetric su1|2 $$ \mathfrak{s}\mathfrak{u}\left(1\Big|2\right) $$ case.