Bonelli, Giulio; Tanzini, Alessandro Topological gauge theories on local spaces and black hole entropy countings. (English) Zbl 1153.83352 Adv. Theor. Math. Phys. 12, No. 6, 1429-1446 (2008). Summary: 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 arXiv: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. Cited in 18 Documents MSC: 83C57 Black holes 81T13 Yang-Mills and other gauge theories in quantum field theory 81T45 Topological field theories in quantum mechanics × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid