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Superspin Chains Solutions from 4D Chern-Simons Theory

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arxiv 2309.04337 v2 pith:BECBGX4V submitted 2023-09-08 hep-th

Youssra Boujakhrout , El Hassan Saidi , Rachid Ahl Laamara , Lalla Btissam Drissi This is my paper
classification hep-th
keywords chainsgaugesuperspintheorychern-simonsoscillatorsupersuperalgebras
verification ladder T0 review T1 audit T2 compute T3 formal
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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 $D(m\mid n)$

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