Operadic formulation of topological vertex algebras and Gerstenhaber or Batalin-Vilkovisky algebras

Abstract

We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric construction of the Batalin-Vilkovisky algebraic structure (or the Gerstenhaber algebra structure) on the cohomology of a topological vertex algebra (or of a weak topological vertex algebra) by combining this operadic formulation with a theorem of Getzler (or of Cohen) which formulates Batalin-Vilkovisky algebras (or Gerstenhaber algebras) in terms of the homology of the framed little disk operad (or of the little disk operad).

42 pages

References in corpus (5)

• Introduction to string field theory
• Closed String Field Theory: Quantum Action and the BV Master Equation
• Batalin-Vilkovisky algebras and two-dimensional topological field theories
• Closed string field theory, strong homotopy Lie algebras and the operad actions of moduli space
• On Some Algebraic Structures Arising in String Theory

Cited by in corpus (8)

• On operad structures of moduli spaces and string theory
• Homotopy Gerstenhaber algebras and topological field theory
• N=2 structures in all string theories
• Introduction to vertex operator algebras I
• Homology of moduli spaces of curves and commutative homotopy algebras
• Infinite Dimensional Geometry and Quantum Field Theory of Strings. II. Infinite Dimensional Noncommutative Geometry of a Self-Interacting String Field
• Untwisting Topological Field Theories
• Semi-infinite forms and topological vertex operator algebras