D-Branes on Toric Calabi-Yau Varieties

Abstract

We analyze B-type D-branes on noncompact toric Calabi--Yau spaces. A general program is presented to find a set of tilting line bundles that yields the associated quiver and its relations. In many cases, this set remains fixed as one moves between phases in the Kähler moduli space. This gives a particularly simple picture of how the derived category remains invariant across all phases. The combinatorial problems involving local cohomology used to determine the tilting set are also related to questions of Pi-stability as one moves between phases. As a result, in some cases precisely those line bundles in the tilting set remain stable over the whole moduli space in some sense.

28 pages, counterexample to global tilting set added, refs added, conventions made more sane

References in corpus (16)

• Phases of $N=2$ Theories In Two Dimensions
• Gauge Theories from Toric Geometry and Brane Tilings
• Calabi-Yau algebras
• Semiorthogonal decomposition for algebraic varieties
• D-Brane Gauge Theories from Toric Singularities and Toric Duality
• The spectrum of BPS branes on a noncompact Calabi-Yau
• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• Seiberg Duality for Quiver Gauge Theories
• Computation of Superpotentials for D-Branes
• String compactifications on Calabi-Yau stacks
• Stability conditions on a non-compact Calabi-Yau threefold
• Superpotentials for Quiver Gauge Theories
• Francia's flip and derived categories
• Cohomology on Toric Varieties and Local Cohomology with Monomial Supports
• Local Cohomology at Monomial Ideals
• A Note on Support in Triangulated Categories

Cited by in corpus (13)

• Wall Crossing, Quivers and Crystals
• Decompactifications and Massless D-Branes in Hybrid Models
• Colored BPS Pyramid Partition Functions, Quivers and Cluster Transformations
• Crepant resolutions and brane tilings I: Toric realization
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• Categories of Massless D-Branes and del Pezzo Surfaces
• Crepant resolutions and brane tilings II: Tilting bundles
• Geometric engineering of (framed) BPS states
• Elusive Worldsheet Instantons in Heterotic String Compactifications
• Probing Geometry with Stability Conditions
• Tilting objects on twisted forms of some relative flag varieties
• Knot Categorification from Mirror Symmetry, Part II: Lagrangians
• Consistently melting crystals