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.
Cite
@article{arxiv.0912.1509,
title = {Instantons, Topological Strings and Enumerative Geometry},
author = {Richard J. Szabo},
journal= {arXiv preprint arXiv:0912.1509},
year = {2015}
}
Comments
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