Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory

Abstract

We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques on its noncommutative deformation. As a result the gauge theory localizes on noncommutative instantons which can be classified in terms of N-coloured three-dimensional Young diagrams. We give to these noncommutative instantons a geometrical description in terms of certain stable framed coherent sheaves on projective space by using a higher-dimensional generalization of the ADHM formalism. From this formalism we construct a topological matrix quantum mechanics which computes an index of BPS states and provides an alternative approach to the six-dimensional gauge theory.

65 pages, 1 figure; v2: References added; v3: Definitions of moduli spaces clarified, references added; Final version to be published in Nuclear Physics B

References in corpus (9)

• The Refined Topological Vertex
• M-theory and a Topological String Duality
• On the partition sum of the NS five-brane
• Non-supersymmetric Black Holes and Topological Strings
• On Wasserstein geometry of the space of Gaussian measures
• Topological Quiver Matrix Models and Quantum Foam
• Noncommutative Instantons on CP^n
• Complex ADHM equations, sheaves on P^3 and quantum instantons
• Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings

Cited by in corpus (5)

• Crystal Melting and Toric Calabi-Yau Manifolds
• Crystal Melting and Wall Crossing Phenomena
• On Framed Quivers, BPS Invariants and Defects
• M theory and the Coulomb phase of higher rank DT invariants
• Quiver matrix model of ADHM type and BPS state counting in diverse dimensions