Expanding the Bethe/Gauge dictionary

Abstract

Abstract We expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N $$ \mathcal{N} $$ = (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 N $$ \mathcal{N} $$ = 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.

Keywords

• Supersymmetric Gauge Theory
• Supersymmetry and Duality
• Field Theories in Lower Dimensions
• Topological Field Theories