Quantum A-infinity Structures for Open-Closed Topological Strings

2006/02/02 by Manfred Herbst, Herbst, Manfred
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.hep-th/0602018

openalex publication_date 2006/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Citations

• Moduli of J-Holomorphic Curves with Lagrangian Boundary Conditions and Open Gromov-Witten Invariants for an S¹-Equivariant Pair
• The analytic geometry of two-dimensional conformal field theory

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