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We study the properties of interacting line defects in the four-dimensionalChern Simons (CS) gauge theory with invariance given by the $SL\left(m|n\right) $ super-group family. From this theory, we derive the oscillatorrealisation of the Lax operator for superspin chains with $SL(m|n)$ symmetry.To this end, we investigate the holomorphic property of the bosonic Laxoperator $\mathcal{L}$ and build a differential equation $%\mathfrak{D}\mathcal{L}=0$ solved by the Costello-Gaioto-Yagi realisation of$\mathcal{L}$ in the framework of\ the CS theory. We generalize thisconstruction to the case of gauge super-groups, and develop a Dynkinsuper-diagram algorithm to\ deal with the decomposition of the Liesuperalgebras. We obtain the generalisation of the Lax operator describing theinteraction between the electric Wilson super-lines and the magnetic 't Hooftsuper-defects. This coupling is given in terms of a mixture of bosonic andfermionic oscillator degrees of freedom in the phase space of magneticallycharged 't Hooft super-lines. The purely fermionic realisation of the superspinchain Lax operator is also investigated and it is found to coincide exactlywith the $\mathbb{Z}_{2}$- gradation of Lie superalgebras.\ \newline Keywords:4D Chern-Simons theory, Super-gauge symmetry, Lie superalgebras and Dynkinsuper-diagrams, Superspin chains and integrability, Super- Lax operator.

Lax Operator and superspin chains from 4D CS gauge theory