Expanding the Bethe/Gauge Dictionary

Abstract

We expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d 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 = 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.

50 pages, 16 figures

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Cited by in corpus (14)

• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• Rational $Q$-systems, Higgsing and Mirror Symmetry
• Gauge/Bethe correspondence from quiver BPS algebras
• 3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve
• Bands and gaps in Nekrasov partition function
• Super-Schur Polynomials for Affine Super Yangian $\mathsf{Y}({\widehat{\mathfrak{gl}}}_{1|1})$
• Bethe/Gauge Correspondence for SO/Sp Gauge Theories and Open Spin Chains
• Nested coordinate Bethe wavefunctions from the Bethe/gauge correspondence
• Spin-$s$ Rational $Q$-system
• di-Langlands correspondence and extended observables
• Line Operators in 4d Chern-Simons Theory and Cherkis Bows
• The Toda system and solution to the $\mathcal{N}$=2 SUSY Yang-Mills theory
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries
• Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical $R$-Matrices for Superspin Chains from the Bethe/Gauge Correspondence