Matrix factorisations and open topological string theory

Abstract

Amplitudes in open topological string theory may be described completely by certain A-infinity-categories. We detail a general construction of all cyclic minimal models for a given A-infinity-algebra and apply this result to the case of N=2 supersymmetric Landau-Ginzburg models. This allows to solve the tree-level theory in the sense that all amplitudes and hence the effective superpotential can be computed algorithmically. Furthermore, the construction provides a novel derivation of the topological metric of such models.

30 pages; v2: three typos corrected

References in corpus (21)

• Phases of $N=2$ Theories In Two Dimensions
• Mirror Manifolds And Topological Field Theory
• Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities
• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• D-Branes, Derived Categories, and Grothendieck Groups
• Derived Categories and Zero-Brane Stability
• Supersymmetry in Boundary Integrable Models
• Computation of Superpotentials for D-Branes
• Superpotentials, A-infinity Relations and WDVV Equations for Open Topological Strings
• On the boundary coupling of topological Landau-Ginzburg models
• Lectures on Noncommutative Geometry
• Localization and traces in open-closed topological Landau-Ginzburg models
• Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I
• Sur les A-infini catégories
• D-brane categories
• Homotopy algebras and noncommutative geometry
• Strongly homotopy algebras of a Kähler manifold
• Topological conformal field theories and Calabi-Yau categories
• Double derivations and Cyclic homology
• Generating the superpotential on a D-brane category: I
• Triangle-generation in topological D-brane categories

Cited by in corpus (13)

• Type II/F-theory Superpotentials with Several Deformations and N=1 Mirror Symmetry
• The Kapustin-Li formula revisited
• D-brane Superpotentials: Geometric and Worldsheet Approaches
• Defect Perturbations in Landau-Ginzburg Models
• Hybrid models for homological projective duals and noncommutative resolutions
• Remarks on quiver gauge theories from open topological string theory
• Calabi-Yau structures on categories of matrix factorizations
• Differential models for B-type open-closed topological Landau-Ginzburg theories
• An invitation to algebraic topological string theory
• Algorithmic deformation of matrix factorisations
• B-type D-branes in hybrid models
• Bulk deformations of open topological string theory
• Constructing $A_{\infty }$-categories of matrix factorisations