New Compact Construction of Eigenstates for Supersymmetric Spin Chains

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.

24 pages; v2: minor changes, published version

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• A review of the AdS/CFT Quantum Spectral Curve
• On Complex Gamma-Function Integrals
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• On Scalar Products in Higher Rank Quantum Separation of Variables
• Form-factors and complete basis of observables via separation of variables for higher rank spin chains
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Solutions of ${\mathfrak{gl}}_{m|n}$ XXX Bethe ansatz equation and rational difference operators
• On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• Separation of variables for higher rank integrable models: review of recent progress