Superspin chains from superstring theory

Abstract

We present a correspondence between two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauge theories and rational integrable $\mathfrak{gl}(m|n)$ spin chains with spin variables taking values in Verma modules. To explain this correspondence, we realize the gauge theories as configurations of branes in string theory and map them by dualities to brane configurations that realize line defects in four-dimensional Chern-Simons theory with gauge group $\mathrm{GL}(m|n)$. The latter configurations embed the superspin chains into superstring theory. We also provide a string theory derivation of a similar correspondence, proposed by Nekrasov, for rational $\mathfrak{gl}(m|n)$ spin chains with spins valued in finite-dimensional representations.

49+14 pages. v2: corrected typos in section 3.4.2

References in corpus (4)

• Ω-deformation and quantization
• Relating Gauge Theories via Gauge/Bethe Correspondence
• Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence
• Wilson-'t Hooft lines as transfer matrices

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• Lax Operator and superspin chains from 4D CS gauge theory
• Superspin Chains Solutions from 4D Chern-Simons Theory
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• Cluster transformations, the tetrahedron equation and three-dimensional gauge theories
• On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
• Line Operators in 4d Chern-Simons Theory and Cherkis Bows
• Complex D($2,1;\zeta$) and spin chain solutions from Chern-Simons theory
• Topological 4D gravity and gravitational defects
• 5d-4d Correspondence in Twisted M-theory on a Conifold
• Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical $R$-Matrices for Superspin Chains from the Bethe/Gauge Correspondence