Instantons, Topological Strings and Enumerative Geometry

Details Instantons, Topological Strings and Enumerative Geometry Instantons, Topological Strings and Enumerative Geometry

2009-12-08

arxiv.org/abs/0912.1509v3

Physics

High Energy Physics

High Energy Physics - Theory

61 pages; v2: Typos corrected, reference added; v3: References added and updated; Invited article for the special issue "Nonli

Scientific paper

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.

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