手性de Rham配合物的susy结构研究进展与问题
Recent advances and open questions on the susy structure of the chiral de Rham Complex
摘要：
本文综述了特殊完整流形上手征de Rham复形的超对称子代数的不同构造。我们描述了基于局域自由鬼系统的全纯-反全纯扇区与基于局域玻色子-费米子系统的左-右扇区分解之间的区别。我们描述了$G_2$和$Spin_7$流形的拓扑扭曲。我们将这些代数的构造描述为李超代数在极小或超主幂零处的量子Hamilton约化。
英文摘要：
We review different constructions of the supersymmetry subalgebras of the chiral de Rham complex on special holonomy manifolds. We describe the difference between the holomorphic-anti-holomorphic sectors based on a local free ghost system vs the decomposition in left-right sectors from a local Boson-Fermion system. We describe the topological twist in the case of $G_2$ and $Spin_7$ manifolds. We describe the construction of these algebras as quantum Hamiltonian reduction of Lie superalgebras at the minimal or superprincipal nilpotent.
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