Stability structures, motivic Donaldson-Thomas invariants and cluster transformations

Abstract

We define new invariants of 3d Calabi-Yau categories endowed with a stability structure. Intuitively, they count the number of semistable objects with fixed class in the K-theory of the category ("number of BPS states with given charge" in physics language). Formally, our motivic DT-invariants are elements of quantum tori over a version of the Grothendieck ring of varieties over the ground field. Via the quasi-classical limit "as the motive of affine line approaches to 1" we obtain numerical DT-invariants which are closely related to those introduced by Behrend. We study some properties of both motivic and numerical DT-invariants including the wall-crossing formulas and integrality. We discuss the relationship with the mathematical works (in the non-triangulated case) of Joyce, Bridgeland and Toledano-Laredo, as well as with works of physicists on Seiberg-Witten model (string junctions), classification of N=2 supersymmetric theories (Cecotti-Vafa) and structure of the moduli space of vector multiplets. Relating the theory of 3d Calabi-Yau categories with distinguished set of generators (called cluster collection) with the theory of quivers with potential we found the connection with cluster transformations and cluster varieties (both classical and quantum).

148 pages

References in corpus (35)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Four-dimensional wall-crossing via three-dimensional field theory
• D-Branes And Mirror Symmetry
• Calabi-Yau algebras
• Curve counting via stable pairs in the derived category
• The quantum dilogarithm and representations quantum cluster varieties
• Dirichlet branes, homological mirror symmetry, and stability
• Donaldson-Thomas invariants via microlocal geometry
• The 3-fold vertex via stable pairs
• Generators and representability of functors in commutative and noncommutative geometry
• Cubics, Integrable Systems, and Calabi-Yau Threefolds
• Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I
• Stability conditions and Stokes factors
• Stability conditions on triangulated categories
• Wall Crossing, Discrete Attractor Flow and Borcherds Algebra
• Holomorphic generating functions for invariants counting coherent sheaves on Calabi-Yau 3-folds
• Crossing the Wall: Branes vs. Bundles
• Derived categories of small toric Calabi-Yau 3-folds and counting invariants
• Mirror Symmetry via Logarithmic Degeneration Data I
• Cohomology of non-commutative Hilbert schemes
• Moment maps, monodromy and mirror manifolds
• Symmetric obstruction theories and Hilbert schemes of points on threefolds
• XI Solomon Lefschetz Memorial Lecture Series: Hodge structures in non-commutative geometry. (Notes by Ernesto Lupercio)
• Generating the superpotential on a D-brane category: I
• A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations
• The A-infinity Deformation Theory of a Point and the Derived Categories of Local Calabi-Yaus
• The universal Euler characteristic for varieties of characteristic zero
• Mutations for quivers with potentials: Oberwolfach talk, April 2007
• Birational Calabi-Yau 3-folds and BPS state counting
• Motivic invariants of Artin stacks and 'stack functions'
• Unital $A_{\infty }$-categories
• Topologies on a triangulated category
• Stability conditions and the braid group
• Derived Hall Algebras
• Functoriality in resolution of singularities

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