On the structure of open-closed topological field theory in two dimensions
arXiv:hep-th/0010269 · doi:10.1016/S0550-3213(01)00135-3
Abstract
I discuss the general formalism of two-dimensional topological field theories defined on open-closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for the identification of the algebraic structure governing such systems. I give a careful treatment of bulk-boundary and boundary-bulk correspondences, which are responsible for the relation between the closed and open sectors. The fact that these correspondences need not be injective nor surjective has interesting implications for the problem of classifying `boundary conditions'. In particular, I give a clear geometric derivation of the (topological) boundary state formalism and point out some of its limitations. Finally, I formulate the problem of classifying (on-shell) boundary extensions of a given closed topological field theory in purely algebraic terms and discuss their reducibility.
38 pages, 17 figures; v2: typos corrected, references updated. This is essentially the final version published in NPB in 2001
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- D-Branes in Landau-Ginzburg Models and Algebraic Geometry
- Construction of two-dimensional topological field theories with non-invertible symmetries
- 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
- Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras
- Cardy algebras and sewing constraints, I
- Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications
- Landau-Ginzburg Realization of Open String TFT
- Localization and traces in open-closed topological Landau-Ginzburg models
- Topological dualities in the Ising model
- Enhanced D-Brane Categories from String Field Theory
- Adjunctions and defects in Landau-Ginzburg models
- Open-string vertex algebras, tensor categories and operads
- Some Comments on Branes, G-flux, and K-theory
- Stability of Landau-Ginzburg branes
- A proposal for 3d quantum gravity and its bulk factorization
- K-Theory from a physical perspective
- Generalized complexes and string field theory
- On the relation between open and closed topological strings
- 3-dimensional defect TQFTs and their tricategories
- Closed/open string diagrammatics
- D-brane categories
- Marginal Deformations of N=4 SYM from Open/Closed Twistor Strings
- State sum construction of two-dimensional open-closed Topological Quantum Field Theories
- D-brane effective action and tachyon condensation in topological minimal models
- Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions
- Topological Field Theory with Haagerup Symmetry
- Massless and Massive Three Dimensional Super Yang-Mills Theory and Mini-Twistor String Theory
- The ABCD of topological recursion
- D-brane instantons and the effective field theory of flux compactifications
- Holomorphic potentials for graded D-branes
- Lectures on Mirror Symmetry, Derived Categories, and D-branes
- Topological Open Membranes
- On the Open-Closed B-Model
- Deformations of Closed Strings and Topological Open Membranes
- Graded Lagrangians, exotic topological D-branes and enhanced triangulated categories
- Cardy condition for open-closed field algebras
- Lecture notes on 2-dimensional defect TQFT
- Frobenius algebras and planar open string topological field theories
- Cardy algebras and sewing constraints, II
- Matrix Factorizations, Minimal Models and Massey Products
- Topological Field Theory and Matrix Product States
- Boundary Conditions for Topological Quantum Field Theories, Anomalies and Projective Modular Functors
- Higher categorical aspects of Hall Algebras
- Instanton Geometry and Quantum A-infinity structure on the Elliptic Curve
- Quantum A-infinity Structures for Open-Closed Topological Strings
- Multi-matrix models and Noncommutative Frobenius algebras obtained from symmetric groups and Brauer algebras
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- A Hurwitz theory avatar of open-closed strings
- Topological D-Branes and Commutative Algebra
- D-Branes in Topological String Theory
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- Cyclic Foam Topological Field Theories
- Generating the superpotential on a D-brane category: I
- Smooth Functorial Field Theories from B-Fields and D-Branes
- On the non-commutative geometry of topological D-branes
- Topological field theories on open-closed -spin surfaces
- Operads and moduli spaces
- Bulk from boundary in finite CFT by means of pivotal module categories
- Extention cohomological fields theories and noncommutative Frobenius manifolds
- Cardy-Frobenius extension of algebra of cut-and-join operators
- Calabi-Yau structures on categories of matrix factorizations
- Differential models for B-type open-closed topological Landau-Ginzburg theories
- Graded D-branes and skew-categories
- Symmetries and defects in three-dimensional topological field theory
- On B-type open-closed Landau-Ginzburg theories defined on Calabi-Yau Stein manifolds
- D-branes and Vector Bundles on Calabi-Yau Manifolds: a view from the Helix
- Topological Correlators in Landau-Ginzburg Models with Boundaries
- Entanglement entropy and edge modes in topological string theory: I
- Noncommutative aspects of open/closed strings via foliations
- Asymptotic Hurwitz numbers
- Non-degeneracy of cohomological traces for general Landau-Ginzburg models
- Pairings in mirror symmetry between a symplectic manifold and a Landau-Ginzburg -model
- Open-Closed String Correspondence in Open String Field Theory
- Matrix Model and String Field Theory
- Algorithmic deformation of matrix factorisations
- Open-closed 3d gravity as a random ensemble
- Open/Closed Topological CP1 Sigma Model Revisited
- Multi-trace Correlators from Permutations as Moduli Space
- The Cyclic and Modular Microcosm Principle in Quantum Topology
- Bulk deformations of open topological string theory
- B-type Landau-Ginzburg models with one-dimensional target
- B-type Landau-Ginzburg models on Stein manifolds
- Truncated affine Rozansky--Witten models as extended defect TQFTs