01205nas a2200109 4500008004300000245008000043210006900123520082300192100002001015700002401035856003601059 2008 en_Ud 00aTopological Gauge Theories on Local Spaces and Black Hole Entropy Countings0 aTopological Gauge Theories on Local Spaces and Black Hole Entrop3 aWe 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 fluctuations 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.1 aBonelli, Giulio1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/1992