论文标题
Poisson Sigma模型和变形量化的全息理论
A holography theory of Poisson sigma model and deformation quantization
论文作者
论文摘要
我们使用托有托司孔结构编码的$ l_ \ infty $代数来构建一种理论的chern-simons类型。 Batalin-Vilkovisky框架内的变形量化是通过在Fulton-Macpherson压缩配置空间上构造Dirichlet边界条件的传播器来执行的。我们的结果表明，BV量化与繁殖器中的几个量规选择无关，这导致全球可观察物是托有泊松结构的几何不变的候选者和世界表结构的拓扑不变性。在局部可观察到的水平上，已经确定了瑞士冠代数结构。如果泊松结构是符合性的，则二维理论对边界理论是同义的。这在经典案例中是已知的，我们确认量子同型也存在。
We construct a Chern-Simons type of theory using the $l_\infty$ algebra encoded by a Poisson structure on arbitrary Riemann surfaces with boundaries. A deformation quantization within the Batalin-Vilkovisky framework is performed by constructing propagators with Dirichlet boundary condition on Fulton-MacPherson compactified configuration space. Our results show that the BV quantization is independent of several gauge choices in propagators, which leads to global observables that are candidates for geometric invariants of Poisson structure and topological invariants for the worldsheet structure. At the level of local observables, a Swiss-Cheese algebra structure has been identified. If the Poisson structure is symplectic, the two-dimensional theory is homotopic to a boundary theory. This is known in the classical case, and we confirm that the quantum homotopy exists as well.
