开闭模空间及其代数结构
Open-closed moduli spaces and related algebraic structures
摘要：
我们建立了开闭弦理论的Batalin-Vilkovisky量子主方程，并证明了相应的模空间产生了一个解，一个基本链的生成函数。该方程编码的拓扑结构的紧化的模空间的边界黎曼曲面。期望加边J-全纯曲线的模空间满足相同的方程，并从这个观点出发，本文讨论了目标空间为点的情况。我们还引入了对称开闭拓扑共形域论的概念，并研究了与之相关的L_ \infty和A_ \infty的代数结构。
英文摘要：
We set up a Batalin-Vilkovisky Quantum Master Equation for open-closed string theory and show that the corresponding moduli spaces give rise to a solution, a generating function for their fundamental chains. The equation encodes the topological structure of the compactification of the moduli space of bordered Riemann surfaces. The moduli spaces of bordered J-holomorphic curves are expected to satisfy the same equation, and from this viewpoint, our paper treats the case of the target space equal to a point. We also introduce the notion of a symmetric Open-Closed Topological Conformal Field Theory and study the L_\infty and A_\infty algebraic structures associated to it.
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