New Compact Construction of Eigenstates for Supersymmetric Spin Chains

TL;DR

This paper introduces a new, compact method for constructing eigenstates in supersymmetric spin chains, simplifying calculations related to integrable models in theoretical physics.

Contribution

It provides a simplified eigenstate construction for supersymmetric spin chains that avoids complex sums over auxiliary roots, extending previous methods to su(1|2).

Findings

Compact eigenstate formula without sums over auxiliary roots

Extension of SoV construction from su(n) to su(1|2)

Simplified calculation of correlation functions in N=4 SYM

Abstract

The problem of separation of variables (SoV) in supersymmetric spin chains is closely related to the calculation of correlation functions in 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 Bg(u_k) operator to the reference state for each of the magnons, in complete analogy with the su(2) algebraic Bethe ansatz. This generalizes our SoV based construction for su(n) to the supersymmetric su(1|2) case.