Duality in Topological Quantum Field Theories

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This thesis presents a thorough analysis of the links between the N=4 supersymmetric gauge theory in four dimensions and its three topological twisted counterparts. Special emphasis is put in deriving explicit results in terms of the vacuum structure and low-energy effective description of four-dimensional supersymmetric gauge theories. A key ingredient is the realization of Montonten-Olive duality in the twisted theories, which is discussed in detail from different viewpoints.
Doctoral Thesis, LaTex2e, 157 pages, uses amsmath and epsfig packages, 1 PostScript figure. Revised version: typos corrected, discussion on Vafa-Witten partition function improved

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