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.

arXiv comment49+14 pages. v2: corrected typos in section 3.4.2

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• 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
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• 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