Open-closed moduli spaces and related algebraic structures

Harrelson, Eric; Voronov, Alexander A.; Zuniga, J. Javier

Open-closed moduli spaces and related algebraic structures

Authors

Harrelson, Eric

Voronov, Alexander A.

Zuniga, J. Javier

Description

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.
21 pages, LaTeX, 4 figures; section on algebraic structures revised