Supersymmetric Noether Currents and Seiberg-Witten Theory : Computation of the Central Charge of the N=2 D=4 Yang-Mills Gauge Theory

The practical implementation of general symmetry principles in the context of effective theories or, more generally, theories with a non-standard phase-space and unusual Lagrangians is often a difficult task that leads to new insights. In this work we deal with an important supersymmetric model the N=2 pure Yang-Mills effective gauge theory -- a four-dimensional non-trivial fully integrable quantum field theory, as shown by Seiberg and Witten -- and construct its supersymmetry currents. The study was carried on with a precise goal in mind that is the computation of the central charge of the model that is the ``meeting point'' of all types of charges and symmetries present in the theory: supersymmetry, gauge (spontaneously broken) symmetry, topological charges and (discrete) electro-magnetic duality symmetry. The richness of the model, the vast areas of application of the method employed (Noether theorem) and the explicit and careful explanation of every detail, make many aspects of the results reported here directly or indirectly applicable to disparate areas of the theoretical investigation of symmetries.