Lectures on D-branes and Sheaves
arXiv:hep-th/0307245
Abstract
These notes are a writeup of lectures given at the twelfth Oporto meeting on ``Geometry, Topology, and Physics,'' and at the Adelaide workshop ``Strings and Mathematics 2003,'' primarily geared towards a physics audience. We review current work relating boundary states in the open string B model on Calabi-Yau manifolds to sheaves. Such relationships provide us with a mechanism for counting open string states in situations where the physical spectrum calculation is nearly intractable -- after translating to mathematics, such calculations become easy. We describe several different approaches to these models, and also describe how these models are changed by varying physical circumstances -- flat B field backgrounds, orbifolds, and nonzero Higgs vevs. We also discuss mathematical interpretations of operator products, and how such mathematical interpretations can be checked physically. One of the motivations for this work is to understand the precise physical relationship between boundary states in the open string B model and derived categories in mathematics, and we outline what is currently known of the relationship.
87 pages, LaTeX, 1 figure; v2: material on Freed-Witten added
References in corpus (28)
- D-branes, Quivers, and ALE Instantons
- Tachyon Condensation on the Brane Antibrane System
- Mirror Manifolds And Topological Field Theory
- Orbifold Resolution by D-Branes
- D-branes in the WZW model
- Lectures on Special Lagrangian Submanifolds
- Open string instantons and superpotentials
- D-branes and Discrete Torsion II
- Supersymmetric Three-cycles and (Super)symmetry Breaking
- D-Branes, Derived Categories, and Grothendieck Groups
- Open Strings and D-branes in WZNW model
- Derived Categories and Zero-Brane Stability
- D-branes, open string vertex operators, and Ext groups
- D-Brane Stability and Monodromy
- Discrete Torsion
- The Mukai pairing, I: the Hochschild structure
- Enhanced D-Brane Categories from String Field Theory
- Chern character in twisted K-theory: equivariant and holomorphic cases
- Stability conditions on triangulated categories
- K-Theory from a physical perspective
- Generalized complexes and string field theory
- Chiral Rings Do Not Suffice: N=(2,2) Theories with Nonzero Fundamental Group
- Massless D-Branes on Calabi-Yau Threefolds and Monodromy
- D-branes, orbifolds, and Ext groups
- Graded Lagrangians, exotic topological D-branes and enhanced triangulated categories
- Solitons in Seiberg-Witten Theory and D-branes in the Derived Category
- String Orbifolds and Quotient Stacks
- D-Branes and Scheme Theory
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- Non-birational twisted derived equivalences in abelian GLSMs
- Lectures on curved beta-gamma systems, pure spinors, and anomalies
- Yukawa Couplings in F-theory and Non-Commutative Geometry
- Deformations of calibrated D-branes in flux generalized complex manifolds
- Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String
- Wall Crossing, Quivers and Crystals
- D-branes, orbifolds, and Ext groups
- New N=1 dualities from orientifold transitions - Part II: String Theory
- Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
- B-branes and supersymmetric quivers in 2d
- Toric geometry and local Calabi-Yau varieties: An introduction to toric geometry (for physicists)
- General aspects of heterotic string compactifications on stacks and gerbes
- Four Kahler Moduli Stabilisation in type IIB Orientifolds with K3-fibred Calabi-Yau threefold compactification
- D-brane instantons on non-Spin cycles
- Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
- D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck
- Special Geometry and Mirror Symmetry for Open String Backgrounds with N=1 Supersymmetry
- D-Branes in Topological String Theory
- 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
- Generalized Toric Polygons, T-branes, and 5d SCFTs
- Knot Categorification from Mirror Symmetry, Part I: Coherent Sheaves
- D-branes, obstructed curves, and minimal model superpotentials
- Derived categories and stacks in physics
- Domain walls and M2-branes partition functions: M-theory and ABJM Theory
- Matrix Factorizations for Local F-Theory Models
- B-branes and the Derived Category
- Line bundle twisted chiral de Rham complex and bound states of D-branes on toric manifolds
- BRST-Invariant Deformations of Geometric Structures in Sigma Models