D-branes, Categories and N=1 Supersymmetry

Abstract

We show that boundary conditions in topological open string theory on Calabi-Yau manifolds are objects in the derived category of coherent sheaves, as foreseen in the homological mirror symmetry proposal of Kontsevich. Together with conformal field theory considerations, this leads to a precise criterion determining the BPS branes at any point in CY moduli space, completing the proposal of Pi-stability.

harvmac, 41 pp., 2 figures. (v4: corrected errors; added explanations)

References in corpus (13)

• Supergravity flows and D-brane stability
• Open string instantons and superpotentials
• The spectrum of BPS branes on a noncompact Calabi-Yau
• Phases of Supersymmetric D-branes on Kaehler Manifolds and the McKay correspondence
• Hypergeometric functions and mirror symmetry in toric varieties
• D-branes on Stringy Calabi-Yau Manifolds
• D-branes, Exceptional Sheaves and Quivers on Calabi-Yau manifolds: From Mukai to McKay
• Vertex Algebras, Mirror Symmetry, And D-Branes: The Case Of Complex Tori
• Topics in D-geometry
• D-branes on Calabi-Yau manifolds and helices
• Derived categories for the working mathematician
• Brane-Antibrane Systems on Calabi-Yau Spaces
• Mirror symmetry and actions of braid groups on derived categories

Cited by in corpus (138)

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• Quantum Quivers and Hall/Hole Halos
• Precision Counting of Small Black Holes
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• Magnetic Monopole Dynamics, Supersymmetry, and Duality
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• The Branes Behind Generalized Symmetry Operators
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• Computation of Superpotentials for D-Branes
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• String compactifications on Calabi-Yau stacks
• Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes
• Permutation Branes
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• Dibaryons from Exceptional Collections
• Landau-Ginzburg Realization of Open String TFT
• D-branes from Matrix Factorizations
• D3/D7 Branes at Singularities: Constraints from Global Embedding and Moduli Stabilisation
• Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String
• GLSM's for partial flag manifolds
• Matrix factorisations and permutation branes
• Local string models of soft supersymmetry breaking
• Twistor Approach to String Compactifications: a Review
• Stability and duality in N=2 supergravity
• D3-instantons, Mock Theta Series and Twistors
• K3 surfaces, modular forms, and non-geometric heterotic compactifications
• Stability of Landau-Ginzburg branes
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• Quantum moduli spaces from matrix models
• Superpotentials for Quiver Gauge Theories
• Seiberg Duality is an Exceptional Mutation
• The Standard Model Quiver in de Sitter String Compactifications
• T-branes as branes within branes
• Coisotropic D8-branes and Model-building
• Effective superpotentials for compact D5-brane Calabi-Yau geometries
• Connecting Solutions in Open String Field Theory with Singular Gauge Transformations
• Gauge-Mediated Supersymmetry Breaking in String Compactifications
• A Point's Point of View of Stringy Geometry
• Multiple D3-instantons and mock modular forms I
• Closed/open string diagrammatics
• D-Branes on Vanishing del Pezzo Surfaces
• The BPS Spectrum of N=2 SU(N) SYM and Parton Branes
• Massless D-Branes on Calabi-Yau Threefolds and Monodromy
• Exceptional Sequences of Invertible Sheaves on Rational Surfaces
• Infinite Distances and the Axion Weak Gravity Conjecture
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• Quantum periods of Calabi-Yau fourfolds
• Tachyon Condensation on the Elliptic Curve
• Decompactifications and Massless D-Branes in Hybrid Models
• The Landau-Ginzburg to Calabi-Yau Dictionary for D-Branes
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• Limit stable objects on Calabi-Yau 3-folds
• New N=1 dualities from orientifold transitions - Part II: String Theory
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• Some Navigation Rules for D-Brane Monodromy
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• Non-perturbative effects and wall-crossing from topological strings
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• Categories of Massless D-Branes and del Pezzo Surfaces
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• Stability conditions on product threefolds of projective spaces and Abelian varieties
• The Web of D-branes at Singularities in Compact Calabi-Yau Manifolds
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• Strings on conifolds from strong coupling dynamics, part I
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• Holomorphic field theories and Calabi--Yau algebras
• Geometric engineering on flops of length two
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• Monopole operators, moduli spaces and dualities
• Seiberg duality for Chern-Simons quivers and D-brane mutations
• The duality between F-theory and the Heterotic String in $D=8$ with two Wilson lines
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• On stability manifolds of Calabi-Yau surfaces
• The Breakdown of Topology at Small Scales
• An analytic torsion for graded D-branes
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