Superspin Chains Solutions from 4D Chern-Simons Theory

TL;DR

This paper extends the 2D integrable systems and 4D Chern-Simons theory correspondence to superspin chains, using super gauge theory and Lie superalgebra gradings to derive new Lax operators.

Contribution

It introduces a novel gauge theory approach to superspin chains and constructs graded oscillator Lax matrices for various Lie superalgebras.

Findings

Derived oscillator Lax operators from 4D Chern-Simons theory.

Established correspondence between superspin chains and super gauge defects.

Constructed graded Lax matrices for multiple Lie superalgebras.

Abstract

As a generalisation of the correspondence linking 2D integrable systems with 4D Chern-Simons (CS) gauge theory, superspin chains are realized by means of crossing electric and magnetic super line defects in the 4D CS with super gauge symmetry. The oscillator realization of Lax operators solving the RLL relations of integrability is obtained in the gauge theory by extending the notion of Levi decomposition to Lie superalgebras. Based on particular 3-gradings of Lie superalgebras, we obtain graded oscillator Lax matrices for superspin chains with internal symmetries given by $A(m-1\mid n-1)$, $B(m\mid n)$, $C(n)$ and $D(m\mid n)$