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• W4296778032 abstract "Abstract We study the properties of interacting line defects in the four-dimensional Chern Simons (CS) gauge theory with invariance given by the <?CDATA $mathrm{S}mathrm{L}left(mvert nright)$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:mi mathvariant=normal>S</mml:mi> <mml:mi mathvariant=normal>L</mml:mi> <mml:mfenced close=) open=(> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo stretchy=false>|</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> </mml:math> super-group family. From this theory, we derive the oscillator realisation of the Lax operator for superspin chains with SL( m | n ) symmetry. To this end, we investigate the holomorphic property of the bosonic Lax operator <?CDATA $mathcal{L}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:mi mathvariant=script>L</mml:mi> </mml:math> and build a differential equation <?CDATA $mathfrak{D}mathcal{L}=0$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:mi mathvariant=fraktur>D</mml:mi> <mml:mi mathvariant=script>L</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:math> solved by the Costello–Gaioto–Yagi realisation of <?CDATA $mathcal{L}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:mi mathvariant=script>L</mml:mi> </mml:math> in the framework of the CS theory. We generalize this construction to the case of gauge super-groups, and develop a Dynkin super-diagram algorithm to deal with the decomposition of the Lie superalgebras. We obtain the generalisation of the Lax operator describing the interaction between the electric Wilson super-lines and the magnetic ’t Hooft super-defects. This coupling is given in terms of a mixture of bosonic and fermionic oscillator degrees of freedom in the phase space of magnetically charged ’t Hooft super-lines. The purely fermionic realisation of the superspin chain Lax operator is also investigated and it is found to coincide exactly with the <?CDATA ${mathbb{Z}}_{2}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:msub> <mml:mrow> <mml:mi mathvariant=double-struck>Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> -gradation of Lie superalgebras." @default.
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• W4296778032 date "2022-10-05" @default.
• W4296778032 modified "2023-10-18" @default.
• W4296778032 title "Lax operator and superspin chains from 4D CS gauge theory" @default.
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• W4296778032 doi "https://doi.org/10.1088/1751-8121/ac9355" @default.
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