Advances in Theoretical and Mathematical Physics

Volume 12 (2008)

Number 6

Topological gauge theories on local spaces and black hole entropy countings

Pages: 1429 – 1446



Giulio Bonelli

Alessandro Tanzini


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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