Open-closed moduli spaces and related algebraic structures

TL;DR

This paper formulates a Batalin-Vilkovisky Quantum Master Equation for open-closed string theory, linking moduli spaces of bordered Riemann surfaces to algebraic structures, and introduces a symmetric open-closed topological conformal field theory.

Contribution

It establishes a quantum master equation framework for open-closed string moduli spaces and explores associated algebraic structures, including L_infinity and A_infinity algebras.

Findings

Derived a generating function for fundamental chains of moduli spaces.

Connected the quantum master equation to the topology of bordered Riemann surfaces.

Introduced the concept of symmetric open-closed topological conformal field theory.

Abstract

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.