## 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.

Original language | English (US) |
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Pages (from-to) | 1-26 |

Number of pages | 26 |

Journal | Letters in Mathematical Physics |

Volume | 94 |

Issue number | 1 |

DOIs | |

State | Published - 2010 |

### Bibliographical note

Funding Information:Partially supported by NSF and JSPS grants and a University of Minnesota Doctoral Dissertation Fellowship.

## Keywords

- BV algebra
- homotopy algebras
- open-closed moduli space
- quantum master equation
- topological conformal field theory