Abstract
We expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d mathcal{N} = (2, 2) supersymmetric gauge theories to include aspects of the algebraic Bethe ansatz. We construct the wave functions of off-shell Bethe states as orbifold defects in the A-twisted supersymmetric gauge theory and study their correlation functions. We also present an alternative description of off-shell Bethe states as boundary conditions in an effective mathcal{N} = 4 supersymmetric quantum mechanics. Finally, we interpret spin chain R-matrices as correlation functions of Janus interfaces for mass parameters in the supersymmetric quantum mechanics.
Highlights
A fundamental entry in the dictionary is the identification of the eigenstates of the spin chain Hamiltonian with massive vacua of the supersymmetric gauge theory
We present an alternative description of off-shell Bethe states as boundary conditions in an effective N = 4 supersymmetric quantum mechanics
We have focussed on reproducing components of the algebraic Bethe ansatz for spin chains from correlation functions in A-twisted supersymmetric gauge theory and their reduction to partition functions in N = 4 supersymmetric quantum mechanics
Summary
We collect some basic information on the Heisenberg XXX 1 spin chain, 2 where all spins transform in the fundamental representation of su(2). Our notation is designed to match that of supersymmetric gauge theory and differs from standard integrability conventions
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