Phases Of N=2 Theories In 1+1 Dimensions With Boundary

Abstract

We study B-type D-branes in linear sigma models with Abelian gauge groups. The most important finding is the grade restriction rule. It classifies representations of the gauge group on the Chan-Paton factor, which can be used to define a family of D-branes over a region of the Kähler moduli space that connects special points of different character. As an application, we find a precise, transparent relation between D-branes in various geometric phases as well as free orbifold and Landau-Ginzburg points. The result reproduces and unifies many of the earlier mathematical results on equivalences of D-brane categories, including the McKay correspondence and Orlov's construction.

arXiv comment265 pages

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• F-theory on singular spaces
• Three-dimensional topological field theory and symplectic algebraic geometry I
• The Crepant Transformation Conjecture for Toric Complete Intersections
• Combinatorial constructions of derived equivalences
• Quiver Yangian and Supersymmetric Quantum Mechanics
• Real Mirror Symmetry for One-parameter Hypersurfaces
• Landscaping with fluxes and the E8 Yukawa Point in F-theory
• Toroidal and Elliptic Quiver BPS Algebras and Beyond
• Calculations for Mirror Symmetry with D-branes
• Crepant resolutions and open strings
• Boundaries, Vermas, and Factorisation
• Decompactifications and Massless D-Branes in Hybrid Models
• The Pfaffian-Grassmannian equivalence revisited
• D-Branes on Toric Calabi-Yau Varieties
• Matrix factorisations and open topological string theory
• (2,2) and (0,4) Supersymmetric Boundary Conditions in 3d N = 4 Theories and Type IIB Branes
• Categories of Massless D-Branes and del Pezzo Surfaces
• Berry Phase and Supersymmetry
• Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence
• D-brane Superpotentials: Geometric and Worldsheet Approaches
• Homological Projective Duality via Variation of Geometric Invariant Theory Quotients
• $\mathcal{N}=2$ supersymmetric field theories on 3-manifolds with A-type boundaries
• Exact Partition Functions on RP2 and Orientifolds
• Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of Calabi-Yau threefolds
• Morphisms from Azumaya prestable curves with a fundamental module to a projective variety: Topological D-strings as a master object for curves
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• Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
• Supersymmetric indices on $I\times T^2$, elliptic genera and dualities with boundaries
• Exact results for boundaries and domain walls in 2d supersymmetric theories
• D-brane central charge and Landau-Ginzburg orbifolds
• D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck
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• Holography, Matrix Factorizations and K-stability
• Mixed braid group actions from deformations of surface singularities
• A Note on Computations of D-brane Superpotential
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• Duality In Two-Dimensional (2,2) Supersymmetric Non-Abelian Gauge Theories
• Categorical Plücker Formula and Homological Projective Duality
• Topological D-Branes and Commutative Algebra
• Gromov-Witten invariants and localization
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• Mukai flops and P-twists
• 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
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• Remarks on quiver gauge theories from open topological string theory
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• On higher rank coisotropic A-branes
• On genus one fibered Calabi-Yau threefolds with 5-sections
• Knot Categorification from Mirror Symmetry, Part I: Coherent Sheaves
• Birational geometry and derived categories
• Probing Geometry with Stability Conditions
• The homological projective dual of Sym^2 P(V)
• Homological mirror symmetry of Fermat polynomials
• Phase transitions in GLSMs and defects
• Triangle-generation in topological D-brane categories
• Orientifolds and D-branes in N=2 gauged linear sigma models
• Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks
• Singular BPS boundary conditions in $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• Heterotic (0,2) Gepner Models and Related Geometries
• Branes and DAHA Representations
• Mirror Symmetry and Discriminants
• A global mirror symmetry framework for the Landau-Ginzburg/Calabi-Yau correspondence
• Nonabelian mirrors and Gromov-Witten invariants
• Perverse schobers and wall crossing
• Derived equivalences for the flops of type $C_2$ and $A_4^G$ via mutation of semiorthogonal decomposition
• Homological flips and homological flops
• An invitation to algebraic topological string theory
• The generalized roof F(1,2,n): Hodge structures and derived categories
• Knot Categorification from Mirror Symmetry, Part II: Lagrangians
• Discriminants and semi-orthogonal decompositions
• Open Mirror Symmetry for Higher Dimensional Calabi-Yau Hypersurfaces
• The derived category of a graded Gorenstein ring
• A toolkit for defect computations in Landau-Ginzburg models
• D0-brane realizations of the resolution of a reduced singular curve
• Non-Factorizable Branes on the Torus
• Topological D-branes from Descent
• Noncommutative resolutions and CICY quotients from a non-abelian GLSM
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• Les Houches lectures on non-perturbative Seiberg-Witten geometry
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• Stringy Kähler Moduli for the Pfaffian-Grassmannian Correspondence
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