Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings
arXiv:0706.2633
Abstract
We study cohomological gauge theories on total spaces of holomorphic line bundles over complex manifolds and obtain their reduction to the base manifold by U(1) equivariant localization of the path integral. We exemplify this general mechanism by proving via exact path integral localization a reduction for local curves conjectured in hep-th/0411280, relevant to the calculation of black hole entropy/Gromov-Witten invariants. Agreement with the four-dimensional gauge theory is recovered by taking into account in the latter non-trivial contributions coming from one-loop fluctuations determinants at the boundary of the total space. We also study a class of abelian gauge theories on Calabi-Yau local surfaces, describing the quantum foam for the A-model, relevant to the calculation of Donaldson-Thomas invariants.
arXiv comment17 pages
References in corpus (6)
- Quantum Foam and Topological Strings
- Two Dimensional Yang-Mills, Black Holes and Topological Strings
- N=4 Supersymmetric Yang-Mills Theory on a Kaehler Surface
- A DK Phase Transition in q-Deformed Yang-Mills on S^2 and Topological Strings
- The Topological G2 String
- Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles