Lax operator and superspin chains from 4D CS gauge theory

Abstract We study the properties of interacting line defects in four-dimensional Chern Simons (CS) gauge theory with invariance given by S mathvariant="normal">L m | n super-group family. From this theory, we derive oscillator realisation Lax operator for superspin chains SL( m | n ) symmetry. To end, investigate holomorphic property bosonic $\mathcal{L}$?> mathvariant="script">L and build a differential equation $\mathfrak{D}\mathcal{L}=0$?> mathvariant="fraktur">D = 0 solved Costello–Gaioto–Yagi framework CS theory. generalize construction to case super-groups, develop Dynkin super-diagram algorithm deal decomposition Lie superalgebras. obtain generalisation describing interaction between electric Wilson super-lines magnetic ’t Hooft super-defects. This coupling is terms mixture fermionic degrees freedom phase space magnetically charged super-lines. The purely chain also investigated it found coincide exactly ${\mathbb{Z}}_{2}$?> mathvariant="double-struck">Z 2 -gradation