论文标题
用于模块化的Operad和Beilinson-Drinfeld代数的连接总和
Connected sum for modular operads and Beilinson-Drinfeld algebras
论文作者
论文摘要
与字符串理论相关的模块化操作可以配备附加的结构，来自连接的表面总和。在此示例中，我们引入了一般模块化的连接总和的概念。我们表明，连接的总和会在与模块化作业相关的功能空间上诱导交换产物。此外，我们将该产品与Barannikov在此功能空间上存在的Barannikov的非交流性Batalin-Vilkovisky结构相结合，获得了Beilinson-Drinfeld代数。最后，我们使用使用此交换产品定义的指数定义研究量子主方程。
Modular operads relevant to string theory can be equipped with an additional structure, coming from the connected sum of surfaces. Motivated by this example, we introduce a notion of connected sum for general modular operads. We show that a connected sum induces a commutative product on the space of functions associated to the modular operad. Moreover, we combine this product with Barannikov's non-commutative Batalin-Vilkovisky structure present on this space of functions, obtaining a Beilinson-Drinfeld algebra. Finally, we study the quantum master equation using the exponential defined using this commutative product.
