Open-closed moduli spaces and related algebraic structures

Details Open-closed moduli spaces and related algebraic structures Open-closed moduli spaces and related algebraic structures

2007-09-25

arxiv.org/abs/0709.3874v2

Mathematics

Quantum Algebra

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

Scientific paper

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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