Quantum A-infinity Structures for Open-Closed Topological Strings

Abstract

We study factorizations of topological string amplitudes on higher genus Riemann surfaces with multiple boundary components and find quantum A-infinity relations, which are the higher genus analog of the (classical) A-infinity relations on the disk. For topological strings with $\hat{c}=3$ the quantum A-infinity relations are trivially satisfied on a single D-brane, whereas in a multiple D-brane configuration they may be used to compute open higher genus amplitudes recursively from disk amplitudes. This can be helpful in open Gromov--Witten theory in order to determine open string higher genus instanton corrections. Finally, we find that the quantum A-infinity structure cannot quite be recast into a quantum master equation on the open string moduli space.

25 pages, 5 figures, LaTeX2e

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Cited by in corpus (8)

• Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String
• Conformal Field Theory and Algebraic Structure of Gauge Theory
• Quantum Open-Closed Homotopy Algebra and String Field Theory
• Effective superpotentials for B-branes in Landau-Ginzburg models
• Instanton Geometry and Quantum A-infinity structure on the Elliptic Curve
• D-Branes in Topological String Theory
• Classes on compactifications of the moduli space of curves through solutions to the quantum master equation
• Perturbative path-integral of string field and the $A_{\infty }$ structure of the BV master equation