Supersymmetric observables of N=1 Quantum Field Theories on a twisted S^1 x S^3

Recent years have seen a big progress in the understanding of quantum field theories defined in curved backgrounds. In particular, in the presence of supersymmetry it has been possible to derive many exact results for large classes of background manifolds. The thesis will consider a simple N=1 quantum field theory defined on a manifold diffeomorphic to S^1 x S^3, review some known results derived through the technique of dimensional reduction, and extend them to the more general case where the 3-sphere is twisted over the circle. A reformulation of the results in terms of Hopf surfaces and their complex structure parameters will be discussed. This background plays an important role in holography as it corresponds to the boundary of supersymmetric black holes in five-dimensional Anti de Sitter space, with the twisting of the sphere corresponding to rotation parameters.