Open-Closed Moduli Spaces and Related Algebraic Structures

Author: Harrelson Eric   Voronov Alexander   Zúñiga J.  

Publisher: Springer Publishing Company

ISSN: 0377-9017

Source: Letters in Mathematical Physics, Vol.94, Iss.1, 2010-10, pp. : 1-26

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Abstract

We set up a Batalin–Vilkovisky Quantum Master Equation (QME) 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 (OC TCFT) and study the L and A algebraic structures associated to it.