Superpotentials, A-infinity Relations and WDVV Equations for Open Topological Strings

Abstract

We give a systematic derivation of the consistency conditions which constrain open-closed disk amplitudes of topological strings. They include the A-infinity relations (which generalize associativity of the boundary product of topological field theory), as well as certain homotopy versions of bulk-boundary crossing symmetry and Cardy constraint. We discuss integrability of amplitudes with respect to bulk and boundary deformations, and write down the analogs of WDVV equations for the space-time superpotential. We also study the structure of these equations from a string field theory point of view. As an application, we determine the effective superpotential for certain families of D-branes in B-twisted topological minimal models, as a function of both closed and open string moduli. This provides an exact description of tachyon condensation in such models, which allows one to determine the truncation of the open string spectrum in a simple manner.

53 pages

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Cited by in corpus (65)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Open & Closed vs. Pure Open String Disk Amplitudes
• Computation of Superpotentials for D-Branes
• F-term equations near Gepner points
• Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications
• Localization and traces in open-closed topological Landau-Ginzburg models
• Opening Mirror Symmetry on the Quintic
• Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String
• Matrix factorisations and permutation branes
• Matrix Factorizations And Mirror Symmetry: The Cubic Curve
• Stability of Landau-Ginzburg branes
• D-brane superpotentials and RG flows on the quintic
• Superpotentials for Quiver Gauge Theories
• Permutation branes and linear matrix factorisations
• Closed/open string diagrammatics
• On N=1 4d Effective Couplings for F-theory and Heterotic Vacua
• D-brane effective action and tachyon condensation in topological minimal models
• Marginal Deformations of N=4 SYM from Open/Closed Twistor Strings
• The effective action of D-branes in Calabi-Yau orientifold compactifications
• Quantum Open-Closed Homotopy Algebra and String Field Theory
• Super-Chern-Simons Theory as Superstring Theory
• The RR charges of A-type Gepner models
• Open-closed homotopy algebra in mathematical physics
• The matrix factorisations of the D-model
• Matrix factorisations and open topological string theory
• D-brane Superpotentials: Geometric and Worldsheet Approaches
• Effective superpotentials for B-branes in Landau-Ginzburg models
• B-branes and supersymmetric quivers in 2d
• Matrix Factorizations, Minimal Models and Massey Products
• Point-like bounding chains in open Gromov-Witten theory
• Moduli Webs and Superpotentials for Five-Branes
• Matrix Factorizations, D-Branes and their Deformations
• D-branes in Toroidal Orbifolds and Mirror Symmetry
• Semi-Chiral Operators in 4d $\mathcal{N}=1$ Gauge Theories
• D-brane Categories for Orientifolds -- The Landau-Ginzburg Case
• Liouville D-branes in Two-Dimensional Strings and Open String Field Theory
• Instanton Geometry and Quantum A-infinity structure on the Elliptic Curve
• Topological D-Branes and Commutative Algebra
• D-Branes in Topological String Theory
• Generating the superpotential on a D-brane category: I
• On the non-commutative geometry of topological D-branes
• Boundary states, matrix factorisations and correlation functions for the E-models
• Remarks on quiver gauge theories from open topological string theory
• Hybrid models for homological projective duals and noncommutative resolutions
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• The holomorphic anomaly for open string moduli
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• Differential models for B-type open-closed topological Landau-Ginzburg theories
• Triangle-generation in topological D-brane categories
• Matrix Factorizations and Homological Mirror Symmetry on the Torus
• Flat Connections in Open String Mirror Symmetry
• Anti-de Sitter D-brane dynamics
• Permutation Orientifolds
• D-brane Moduli Spaces and Superpotentials in a Two-Parameter Model
• Categories of holomorphic line bundles on higher dimensional noncommutative complex tori
• Deformation Theory of Matrix Factorizations and F-Terms in the Boundary Changing Sector
• Non-commutative moduli spaces of topological D-branes
• Non-Factorizable Branes on the Torus
• Homotopy Relations for Topological VOA
• Algorithmic deformation of matrix factorisations
• B-type D-branes in hybrid models
• The Quantum $A_{\infty }$-Relations on the Elliptic Curve
• On higher order Leibniz identities in TCFT
• Bulk deformations of open topological string theory
• Matrix Factorizations For Non-Abelian Orbifolds