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This book is divided in two parts. The first one which comprises chapter 1 and 2 regards the perturbative inspection of a highly non trivial super-conformal model. I present the explicit computation of a wide class of four point Green functions up to the second order in the gauge coupling. Then using the conformal Operator Product Expansion (OPE) I extract informations about the spectrum (conformal dimensions) and the trilinear couplings of the theory. The second part which comprises chapter 3 and 4 contains some topics concerning instanton computations in supersymmetric gauge theories. In chapter 3 I present a review of the ADHM construction for gauge theories, with and without supersymmetry. Particular emphasis is given to the geometrical meaning of the construction. Chapter 4 contains the application of a Localization Formula to the computation of the instanton partition function. The known results on the unitary gauge group are reviewed in detail. Then I propose some original results concerning the extension of this formalism to the orthogonal and symplectic gauge theories.

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Marco D´Alessandro received his PhD in physics in 2006, with a thesis concerning the analysis of quantum field theories beyond the standard model.He currently works as a researcher, dealing with topics connect to both statistical mechanics and to the interaction between electromagnetic radiation and complex systems.

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