Open-Closed Moduli Spaces and Related Algebraic Structures

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

doi:10.1007/s11005-010-0418-0

Open-Closed Moduli Spaces and Related Algebraic Structures

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

School of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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)
Pages (from-to)	1-26
Number of pages	26
Journal	Letters in Mathematical Physics
Volume	94
Issue number	1
DOIs	https://doi.org/10.1007/s11005-010-0418-0
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

Publisher link

10.1007/s11005-010-0418-0

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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.",

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

author = "Eric Harrelson and Voronov, {Alexander A.} and Z{\'u}{\~n}iga, {J. Javier}",

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doi = "10.1007/s11005-010-0418-0",

language = "English (US)",

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T1 - Open-Closed Moduli Spaces and Related Algebraic Structures

AU - Harrelson, Eric

AU - Voronov, Alexander A.

AU - Zúñiga, J. Javier

N1 - Funding Information: Partially supported by NSF and JSPS grants and a University of Minnesota Doctoral Dissertation Fellowship.

PY - 2010

Y1 - 2010

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

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JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 1

ER -

Open-Closed Moduli Spaces and Related Algebraic Structures

Abstract

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