论文标题
经典的散装对应关系
A Classical Bulk-Boundary Correspondence
论文作者
论文摘要
在本文中，我们使用$ \ mathbb {p} _0 $ - 捕集代数的语言来阐明1）在1）Poisson batalin-vilkovisky（BV）的可观察到的poisson batalin-vilkovisky（bv）理论上的普遍性$ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n y。 \ mathbb {r} _ {\ geq 0} $。这种原型的例子是$ \ mathbb {r} $上的Poisson BV理论，该理论编码了Poisson歧管上函数代数的代数，在泊松歧管上，其上半平面上相关的散装系统是Poisson Sigma模型。通过这种方式，我们获得了基本见解的概括和部分理由，这使Kontsevich对Poisson歧管进行了变形量化。这些结果的证明很大程度上取决于$ \ mathbb {p} _0 $ -Algebras的Operadic同义理论。
In this article, we use the language of $\mathbb{P}_0$-factorization algebras to articulate a classical bulk-boundary correspondence between 1) the observables of a Poisson Batalin-Vilkovisky (BV) theory on a manifold $N$ and 2) the observables of the associated universal bulk-boundary system on $N\times \mathbb{R}_{\geq 0}$. The archetypal such example is the Poisson BV theory on $\mathbb{R}$ encoding the algebra of functions on a Poisson manifold, whose associated bulk-boundary system on the upper half-plane is the Poisson sigma model. In this way, we obtain a generalization and partial justification of the basic insight that led Kontsevich to his deformation quantization of Poisson manifolds. The proof of these results relies significantly on the operadic homotopy theory of $\mathbb{P}_0$-algebras.
