D-Branes And Mirror Symmetry

Abstract

We study (2,2) supersymmetric field theories on two-dimensional worldsheet with boundaries. We determine D-branes (boundary conditions and boundary interactions) that preserve half of the bulk supercharges in non-linear sigma models, gauged linear sigma models, and Landau-Ginzburg models. We identify a mechanism for brane creation in LG theories and provide a new derivation of a link between soliton numbers of the massive theories and R-charges of vacua at the UV fixed point. Moreover we identify Lagrangian submanifolds that arise as the mirror of certain D-branes wrapped around holomorphic cycles of Kähler manifolds. In the case of Fano varieties this leads to the explanation of Helix structure of the collection of exceptional bundles and soliton numbers, through Picard-Lefshetz theory applied to the mirror LG theory. Furthermore using the LG realization of minimal models we find a purely geometric realization of Verlinde Algebra for SU(2) level k as intersection numbers of D-branes. This also leads to a direct computation of modular transformation matrix and provides a geometric interpretation for its role in diagonalizing the Fusion algebra.

106 pages

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Cited by in corpus (252)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Superstrings and Topological Strings at Large N
• Triangulated categories of singularities and D-branes in Landau-Ginzburg models
• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Analytic Continuation Of Chern-Simons Theory
• Quantum Foam and Topological Strings
• Disk Instantons, Mirror Symmetry and the Duality Web
• Worldsheet Derivation of a Large N Duality
• Orientifolds of K3 and Calabi-Yau Manifolds with Intersecting D-branes
• The spectrum of BPS branes on a noncompact Calabi-Yau
• R-Twisting and 4d/2d Correspondences
• Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves
• Aspects of Non-Abelian Gauge Dynamics in Two-Dimensional N=(2,2) Theories
• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• D-terms and F-terms from D7-brane fluxes
• Symmetries of Toric Duality
• Hartle-Hawking Wave-Function for Flux Compactifications
• Wall-Crossing in Coupled 2d-4d Systems
• On the structure of open-closed topological field theory in two dimensions
• Surface Operators in N=2 4d Gauge Theories
• N=2 Quantum Field Theories and Their BPS Quivers
• Derived Categories and Zero-Brane Stability
• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• Orientifolds of Gepner Models
• Quantum Calabi-Yau and Classical Crystals
• F-term equations near Gepner points
• Permutation Branes
• Mirror symmetry for open strings
• D-branes and K-theory in 2D topological field theory
• On the boundary coupling of topological Landau-Ginzburg models
• Counting Chiral Operators in Quiver Gauge Theories
• Moduli Stabilization in Non-Geometric Backgrounds
• Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary
• Minkowski Polynomials and Mutations
• Defects and Bulk Perturbations of Boundary Landau-Ginzburg Orbifolds
• D-branes on Stringy Calabi-Yau Manifolds
• Orientifolds, Mirror Symmetry and Superpotentials
• Braids, Walls, and Mirrors
• N=1 Special Geometry, Mixed Hodge Variations and Toric Geometry
• Dibaryons from Exceptional Collections
• Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications
• Localization and traces in open-closed topological Landau-Ginzburg models
• BPS states and algebras from quivers
• A Stringy Origin of M2 Brane Chern-Simons Theories
• Rational Conformal Field Theories and Complex Multiplication
• D-branes in Topological Minimal Models: the Landau-Ginzburg Approach
• D-branes, Exceptional Sheaves and Quivers on Calabi-Yau manifolds: From Mukai to McKay
• On N=1 Mirror Symmetry for Open Type II Strings
• D-branes from Matrix Factorizations
• Homological mirror symmetry for the quartic surface
• Large N Duality, Mirror Symmetry, and a Q-deformed A-polynomial for Knots
• Enhanced D-Brane Categories from String Field Theory
• Brane Brick Models in the Mirror
• Central charges, symplectic forms, and hypergeometric series in local mirror symmetry
• N=1 supersymmetric sigma model with boundaries, II
• Mirror Symmetry and a $G_2$ Flop
• Resurgence in complex Chern-Simons theory
• $G_2$ Manifolds, Mirror Symmetry and Geometric Engineering
• Worldsheet Descriptions of Wrapped NS Five-Branes
• On Arnold's 14 `exceptional' N=2 superconformal gauge theories
• D-branes on Calabi-Yau Manifolds and Superpotentials
• Some Comments on Branes, G-flux, and K-theory
• Duality Walls, Duality Trees and Fractional Branes
• Mirror symmetry for toric Fano manifolds via SYZ transformations
• Little String Theory and Heterotic/Type II Duality
• Intersection numbers of spectral curves
• Consistent Boundary Conditions for Open Strings
• N=2 Boundary conditions for non-linear sigma models and Landau-Ginzburg models
• Generalized complexes and string field theory
• Enhanced Worldvolume Supersymmetry and Intersecting Domain Walls in N=1 SQCD
• Supersymmetric Boundary Conditions in Three Dimensional N = 2 Theories
• A Point's Point of View of Stringy Geometry
• Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry
• N=1 supersymmetric sigma model with boundaries, I
• A-twisted Landau-Ginzburg models
• Closed/open string diagrammatics
• Brane Tilings and Specular Duality
• The BPS Spectrum of N=2 SU(N) SYM and Parton Branes
• D-brane categories
• D-branes and Normal Functions
• D-brane effective action and tachyon condensation in topological minimal models
• Counting Domain Walls in N=1 Super Yang-Mills Theory
• Wall Crossing, Quivers and Crystals
• The effective action of D-branes in Calabi-Yau orientifold compactifications
• On de Sitter Vacua in Type IIA Orientifold Compactifications
• On Correspondences Between Toric Singularities and (p,q)-webs
• The nonequivariant coherent-constructible correspondence for toric stacks
• The Wave Function Behavior of the Open Topological String Partition Function on the Conifold
• Special Geometry and the Swampland
• Colored Kauffman Homology and Super-A-polynomials
• Conifolds and Geometric Transitions
• The RR charges of A-type Gepner models
• Intersecting D-brane Models
• Open Gromov-Witten invariants, mirror maps, and Seidel representations for toric manifolds
• Disc Instantons in Linear Sigma Models
• Boundaries and Defects of N=4 SYM with 4 Supercharges, Part I: Boundary/Junction Conditions
• Localized Tachyons and the Quantum McKay Correspondence
• Boundaries, Vermas, and Factorisation
• Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I
• Integrable hierarchies and the mirror model of local CP1
• On Decay of K-theory
• More Arnold's N = 2 superconformal gauge theories
• Enumerative meaning of mirror maps for toric Calabi-Yau manifolds
• Open topological strings and integrable hierarchies: Remodeling the A-model
• Quadrality for Supersymmetric Matrix Models
• Strings in Twistor Superspace and Mirror Symmetry
• On the Open-Closed B-Model
• New N=1 dualities from orientifold transitions - Part II: String Theory
• Gauge/Bethe correspondence from quiver BPS algebras
• Local Mirror Symmetry for the Topological Vertex
• Mirror symmetry for weighted projective planes and their noncommutative deformations
• Higher Cluster Categories and QFT Dualities
• (2,2) and (0,4) Supersymmetric Boundary Conditions in 3d N = 4 Theories and Type IIB Branes
• All Genus Open-Closed Mirror Symmetry for Affine Toric Calabi-Yau 3-Orbifolds
• Dimer Models from Mirror Symmetry and Quivering Amoebae
• D-Branes on ALE Spaces and the ADE Classification of Conformal Field Theories
• Crystal Melting and Black Holes
• The Coherent-Constructible Correspondence and Homological Mirror Symmetry for Toric Varieties
• Boundaries and Defects of N=4 SYM with 4 Supercharges, Part II: Brane Constructions and 3d N=2 Field Theories
• $\mathcal{N}=2$ supersymmetric field theories on 3-manifolds with A-type boundaries
• Effective superpotentials for B-branes in Landau-Ginzburg models
• Boundary RG Flows of N=2 Minimal Models
• Azumaya-type noncommutative spaces and morphisms therefrom: Polchinski's D-branes in string theory from Grothendieck's viewpoint
• 2d Wall-Crossing, R-twisting, and a Supersymmetric Index
• N=2 Superconformal boundary states for free bosons and fermions
• Landau-Ginzburg models -- old and new
• Neurons on Amoebae
• Tropical Lagrangian Hypersurfaces are Unobstructed
• Mirror maps equal SYZ maps for toric Calabi-Yau surfaces
• Boundary Rings and N=2 Coset Models
• Calabi's diastasis as interface entropy
• A new kind of McKay correspondence from non-Abelian gauge theories
• Non-compact Topological Branes on Conifold
• The geometry of the limit of N=2 minimal models
• Supersymmetric Boundaries and Junctions in Four Dimensions
• Moduli spaces of Calabi-Yau $d$-folds as gravitational-chiral instantons
• Profiling the Brane Drain in a Nonsupersymmetric Orbifold
• Holomorphic line bundles on projective toric manifolds from Lagrangian sections of their mirrors by SYZ transformations
• Brane Dynamics in CFT Backgrounds
• D-branes in N=2 coset models and twisted equivariant K-theory
• D-brane central charge and Landau-Ginzburg orbifolds
• Stability conditions on $A_n$-singularities
• c < 1 String from Two Dimensional Black Holes
• D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck
• F-theory Duals of M-theory on G2 Manifolds from Mirror Symmetry
• Lectures on D-branes, Gauge Theories and Calabi-Yau Singularities
• Special Geometry and Mirror Symmetry for Open String Backgrounds with N=1 Supersymmetry
• A Note on Computations of D-brane Superpotential
• Geometric Transitions on non-Kaehler Manifolds
• T-duality Transformation of Gauged Linear Sigma Model with F-term
• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
• On Supersymmetry, Boundary Actions and Brane Charges
• $E_6$ Yukawa couplings in F-theory as D-brane instanton effects
• Free Field Construction of D-branes in N=2 Superconformal Minimal Models
• Open String Invariants and Mirror Curve of the Resolved Conifold
• On Algebraic Singularities, Finite Graphs and D-Brane Gauge Theories: A String Theoretic Perspective
• K-theoretical boundary rings in N=2 coset models
• Swampland geometry and the gauge couplings
• Picard-Fuchs Equations for Relative Periods and Abel-Jacobi Map for Calabi-Yau Hypersurfaces
• Bulk perturbations of N=2 branes
• Comments On The Two-Dimensional Landau-Ginzburg Approach To Link Homology
• On Phases of 3d $\mathcal{N}=2$ Chern-Simons-Matter Theories
• Local Calabi-Yau manifolds of type \tilde{A} via SYZ mirror symmetry
• D-branes and Azumaya/matrix noncommutative differential geometry, I: D-branes as fundamental objects in string theory and differentiable maps from Azumaya/matrix manifolds with a fundamental module to real manifolds
• Supersymmetric Boundary Conditions for the N=2 Sigma Model
• BRST construction of D-branes in SU(2) WZW model
• Special Lagrangian fibrations, mirror symmetry and Calabi-Yau double covers
• Tensor Product and Permutation Branes on the Torus
• Obstructions and lines of marginal stability from the world-sheet
• Quantum Deformation Theory of the Airy Curve and Mirror Symmetry of a Point
• Superconformal Index, BPS Monodromy and Chiral Algebras
• Gauged Linear Sigma Model with F-term for A-type ALE Space
• Toric Geometry and String Theory Descriptions of Qudit Systems
• Transformation of algebraic Gromov-Witten invariants of three-folds under flops and small extremal transitions, with an appendix from the stringy and the symplectic viewpoint
• Why Is Landau-Ginzburg Link Cohomology Equivalent To Khovanov Homology?
• Gauged Linear Sigma Model on Supermanifold
• On the Geometry and Homology of Certain Simple Stratified Varieties
• On higher rank coisotropic A-branes
• Boundary fermions and the plane wave
• Parameter Space of Quiver Gauge Theories
• Nontrivial Azumaya noncommutative schemes, morphisms therefrom, and their extension by the sheaf of algebras of differential operators: D-branes in a $B$-field background à la Polchinski-Grothendieck Ansatz
• N=2 boundary supersymmetry in integrable models and perturbed boundary conformal field theory
• The world-sheet description of A and B branes revisited
• Twisted boundary states in Kazama-Suzuki models
• Mirror Symmetry And Quantum Geometry
• Knot Categorification from Mirror Symmetry, Part I: Coherent Sheaves
• On the Classification of Duality Webs for Graded Quivers
• Local B-model Yukawa couplings from A-twisted correlators
• Homological Knot Invariants from Mirror Symmetry
• FQHE and $t{t}^{\ast }$ geometry
• Manifestly Supersymmetric RG Flows
• Crosscap states in N=2 Liouville theory
• Toric Varieties with NC Toric Actions: NC Type IIA Geometry
• A Geometrical Construction of Rational Boundary States in Linear Sigma Models
• $S^1$-fixed-points in hyper-Quot-schemes and an exact mirror formula for flag manifolds from the extended mirror principle diagram
• Chern-Simons matrix model for local conifold
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Fukaya category of Grassmannians: rectangles
• Reconstructing GKZ via topological recursion
• D-branes of A-type, their deformations, and Morse cobordism of A-branes on Calabi-Yau 3-folds under a split attractor flow: Donaldson/Alexander-Hilden-Lozano-Montesinos-Thurston/Hurwitz/Denef-Joyce meeting Polchinski-Grothendieck
• tt* Geometry and a Twistorial Extension of Topological Strings
• Confinement on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and Double-String Collapse
• G_2 Holonomy, Mirror Symmetry and Phases of N=1 SYM
• Phase transitions in GLSMs and defects
• SYZ mirror symmetry for toric varieties
• Lagrangian cobordism in Lefschetz fibrations
• D-branes and Vector Bundles on Calabi-Yau Manifolds: a view from the Helix
• Singular BPS boundary conditions in $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• Landau-Ginzburg Description of D-branes on ALE Spaces
• N=2 Supersymmetric Sigma Models and D-branes
• Geometric transitions, double scaling limits and gauge theories
• Topological Correlators in Landau-Ginzburg Models with Boundaries
• Homological mirror symmetry is T-duality for ${\mathbb{P}}^n$
• Phase space polarization and the topological string: a case study
• Mahler Measure for a Quiver Symphony
• Boundary Weyl anomaly of $\mathcal{N}=(2,2)$ superconformal models
• Categorical Wall-Crossing in Landau-Ginzburg Models
• On Geometric Engineering of Supersymmetric Gauge Theories
• Nonabelian mirrors and Gromov-Witten invariants
• Algebra of the infrared and secondary polytopes
• Linear Models for Flux Vacua
• Unwrapped continuation invariance in Lagrangian Floer theory: energy and $C^0$ estimates
• D0-brane realizations of the resolution of a reduced singular curve
• Kahler Potentials on Toric Varieties
• Floer homology in symplectic geometry and in mirror symmetry
• Integrability of the N=2 boundary sine-Gordon model
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings
• Knot Categorification from Mirror Symmetry, Part II: Lagrangians
• Local B-model and Mixed Hodge Structure
• The Strominger-Yau-Zaslow conjecture and its impact
• Coisotropic Branes in Toric Calabi-Yau 3-folds
• NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion
• Higher Derivative Corrections to the Abelian Born-Infeld Action using Superspace Methods
• Les Houches lectures on non-perturbative Seiberg-Witten geometry
• The Physical Mirror Equivalence for the Local P^2
• Remarks on mirror symmetry of Donaldson-Thomas theory for Calabi-Yau 4-folds
• Chern-Simons theory on spherical Seifert manifolds, topological strings and integrable systems
• Quasimap SYZ for toric Calabi-Yau manifolds
• From primitive form to mirror symmetry
• SYZ mirror symmetry from Witten-Morse theory
• The open string McKay correspondence for type A singularities
• Difference Equations: from Berry Connections to the Coulomb Branch
• A Note on Braid Group Actions on Semiorthonormal Bases of Mukai Lattices
• Topological defects in string theory orbifolds with target spaces $\mathbb{C}/{\mathbb{Z}}_N$ and $S^1/{\mathbb{Z}}_2$
• On Stokes Matrices of Calabi-Yau hypersurfaces
• Local Mirror Symmetry and Type IIA Monodromy of Calabi-Yau manifolds
• D-Branes on C^3_6 part I: prepotential and GW-invariants
• Homological Mirror Symmetry for Toric del Pezzo Surfaces
• On Phases of Generic Toric Singularities
• Algebraic structure of $t{t}^{\ast }$ equations for Calabi-Yau sigma models
• Open Gauged Sigma Models, Equivariant Branes, and Equivariant Homological Mirror Symmetry