Open-Closed Moduli Spaces and Related Algebraic Structures

• DOI: 10.1007/s11005-010-0418-0
• Publication Date: 2010-08-31T05:16:18Z
• Authors: Eric Harrelson; Alexander A. Voronov; J. Javier Zúñiga
• Keywords: 14D21; 81T40; 01 natural sciences; 14D21; Mathematics - Algebraic Geometry; 81T40; Mathematics - Quantum Algebra; 0103 physical sciences; FOS: Mathematics; Quantum Algebra (math.QA); 0101 mathematics; Algebraic Geometry (math.AG)

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.<br/>21 pages, LaTeX, 4 figures; section on algebraic structures revised<br/>