TY - JOUR

T1 - Open-Closed Moduli Spaces and Related Algebraic Structures

AU - Harrelson, Eric

AU - Voronov, Alexander A.

AU - Zúñiga, J. Javier

PY - 2010/9/6

Y1 - 2010/9/6

N2 - 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.

AB - 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.

KW - BV algebra

KW - homotopy algebras

KW - open-closed moduli space

KW - quantum master equation

KW - topological conformal field theory

UR - http://www.scopus.com/inward/record.url?scp=77956125042&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956125042&partnerID=8YFLogxK

U2 - 10.1007/s11005-010-0418-0

DO - 10.1007/s11005-010-0418-0

M3 - Article

AN - SCOPUS:77956125042

VL - 94

SP - 1

EP - 26

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 1

ER -