论文标题
4D CS理论的LAX运算符和超级单链链
Lax Operator and superspin chains from 4D CS gauge theory
论文作者
论文摘要
我们研究了$ sl \ lest（m | n \ right）$ super-group家族的四维Chern Simons（CS）仪表理论中相互作用线缺陷的特性。从这个理论中，我们以$ SL（M | N）$对称性来得出Superspin链的LAX运算符的振荡器实现。 To this end, we investigate the holomorphic property of the bosonic Lax operator $\mathcal{L}$ 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.我们将这种结构推广到量规超组的情况下，并开发出一种Dynkin Super-Dagram算法，以处理Lie Superalgebras的分解。我们获得了LAX操作员的概括，描述了电动Wilson超级线与磁性hooft超级缺陷之间的相互作用。这种耦合是根据磁性带电't Hooft Super-line的相空间中的骨气和费米振荡器自由度的混合物的。还研究了Superspin链lax操作员的纯粹的效费用实现，并发现它与$ \ Mathbb {z} _ {2} $ - lie superalgebras的级别。超级宽松的操作员。
We study the properties of interacting line defects in the four-dimensional Chern Simons (CS) gauge theory with invariance given by the $SL\left( m|n\right) $ 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 $\mathcal{L}$ 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 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 $\mathbb{Z}_{2}$- gradation of Lie superalgebras.\ \newline Keywords: 4D Chern-Simons theory, Super-gauge symmetry, Lie superalgebras and Dynkin super-diagrams, Superspin chains and integrability, Super- Lax operator.
