Instantons, Topological Strings and Enumerative Geometry

Abstract

We review and elaborate on certain aspects of the connections between instanton counting in maximally supersymmetric gauge theories and the computation of enumerative invariants of smooth varieties. We study in detail three instances of gauge theories in six, four and two dimensions which naturally arise in the context of topological string theory on certain non-compact threefolds. We describe how the instanton counting in these gauge theories are related to the computation of the entropy of supersymmetric black holes, and how these results are related to wall-crossing properties of enumerative invariants such as Donaldson-Thomas and Gromov-Witten invariants. Some features of moduli spaces of torsion-free sheaves and the computation of their Euler characteristics are also elucidated.

61 pages; v2: Typos corrected, reference added; v3: References added and updated; Invited article for the special issue "Nonlinear and Noncommutative Mathematics: New Developments and Applications in Quantum Physics" of Advances in Mathematical Physics

References in corpus (4)

• Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
• Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
• Instantons and Donaldson-Thomas Invariants
• Local holomorphic Euler characteristic and instanton decay

Cited by in corpus (15)

• Wall-crossing of D4-D2-D0 and flop of the conifold
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
• $T\overline{T}$-deformation of $q$-Yang-Mills theory
• Statistical model and BPS D4-D2-D0 counting
• Multiple D4-D2-D0 on the Conifold and Wall-crossing with the Flop
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• A note on statistical model for BPS D4-D2-D0 states
• Quivers, Line Defects and Framed BPS Invariants
• Matrix models and stochastic growth in Donaldson-Thomas theory
• Evidence for Duality of Conifold from Fundamental String
• On Framed Quivers, BPS Invariants and Defects
• Mahler Measure for a Quiver Symphony
• Lattice random walks and quantum A-period conjecture
• M theory and the Coulomb phase of higher rank DT invariants