Advances in Theoretical and Mathematical Physics
- Adv. Theor. Math. Phys.
- Volume 12, Number 6 (2008), 1429-1446.
Topological gauge theories on local spaces and black hole entropy countings
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 fluctuation 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.
Adv. Theor. Math. Phys., Volume 12, Number 6 (2008), 1429-1446.
First available in Project Euclid: 19 September 2008
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Bonelli, Giulio; Tanzini, Alessandro. Topological gauge theories on local spaces and black hole entropy countings. Adv. Theor. Math. Phys. 12 (2008), no. 6, 1429--1446. https://projecteuclid.org/euclid.atmp/1221834537