Open-Closed Moduli Spaces and Related Algebraic Structures

Eric Harrelson, Alexander A. Voronov, J. Javier Zúñiga

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 languageEnglish (US)
Pages (from-to)1-26
Number of pages26
JournalLetters in Mathematical Physics
Issue number1
StatePublished - 2010

Bibliographical note

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


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


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