## Advances in Theoretical and Mathematical Physics

### Topological gauge theories on local spaces and black hole entropy countings

#### 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 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.

#### Article information

Source
Adv. Theor. Math. Phys., Volume 12, Number 6 (2008), 1429-1446.

Dates
First available in Project Euclid: 19 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1221834537

Mathematical Reviews number (MathSciNet)
MR2443269

Zentralblatt MATH identifier
1153.83352

#### Citation

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