Advances in Theoretical and Mathematical Physics

Topological gauge theories on local spaces and black hole entropy countings

Giulio Bonelli and Alessandro Tanzini

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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.

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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.

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