The complete renormalization procedure of a general N = 1 supersymmetric gauge theory in the Wess-Zumino gauge is presented, using the regulator free "algebraic renormalization" procedure. Both gauge invariance and supersymmetry are included into one single BRS invariance. The form of the general nonabelian anomaly is given. Furthermore, it is explained how the gauge BRS and the supersymmetry functional operators can be extracted from the general BRS operator. It is then shown that the supersymmetry operators actually belong to the closed, finite, Wess-Zumino superalgebra when their action is restricted to the space of the "gauge invariant operators", i.e. to the cohomology classes of the gauge BRS operator.
We develop a superspace Noether procedure for supersymmetric field theories
in 4-dimensions for which an off-shell formulation in ordinary superspace
exists. In this way we obtain an elegant and compact derivation of the various
supercurrents in these theories. We then apply this formalism to compute the
central charges for a variety of effective actions. As a by-product we also
obtain a simple derivation of the anomalous superconformal Ward-identity in N=2
Yang-Mills theory. The connection with linearized supergravity is also
discussed.Comment: 47 pages, Latex, improved pedagogical presentation and references
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We provide N = 1 Super Yang-Mills theory in the Wess-Zumino gauge with mass terms for the supersymmetric partners of the gauge fields and of the matter fields, together with a supersymmetric mass term for the fermionic matter fields. All mass terms are chosen in such a way to induce soft supersymmetry breakings at most, while preserving gauge invariance to all orders of perturbation theory. The breakings are controlled through an extended Slavnov-Taylor identity. The renormalization analysis, both in the ultraviolet and in the infrared region, is performed.
The central charge in the N = 2 super-Yang-Mills theory plays an essential role in the work of Seiberg and Witten as it gives the mass spectrum of the BPS states of the quantum theory. Our aim in this letter is to present a direct computation of this central charge for the leading order (in a momentum expansion) of the effective action. We will consider the N = 2 super-Yang-Mills theory with gauge group SU(2). The leading order of the effective action is given by the same holomorphic function F appearing in the low energy U(1) effective action.
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