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We show how to consistently renormalize $mathcal{N} = 1$ and $mathcal{N} = 2$ super-Yang-Mills theories in flat space with a local (i.e. space-time-dependent) renormalization scale in a holomorphic scheme. The action gets enhanced by a term proportional to derivatives of the holomorphic coupling. In the $mathcal{N} = 2$ case, this new action is exact at all orders in perturbation theory.
The renormalization of N=1 Super Yang-Mills theory is analysed in the Wess-Zumino gauge, employing the Landau condition. An all orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only thr
Quantum properties of topological Yang-Mills theory in (anti-)self-dual Landau gauge were recently investigated by the authors. We extend the analysis of renormalizability for two generalized classes of gauges; each of them depending on one gauge par
We reconstruct the action of $N=1, D=4$ Wess-Zumino and $N=1, 2, D=4$ super-Yang-Mills theories, using integral top forms on the supermanifold ${cal M}^{(4|4)}$. Choosing different Picture Changing Operators, we show the equivalence of their rheonomi
We construct the 4-dimensional ${cal N}=frac12$ and ${cal N}=1$ inhomogeneously mass-deformed super Yang-Mills theories from the ${cal N} =1^*$ and ${cal N} =2^*$ theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is at
We calculate one-loop scattering amplitudes in N=4 super Yang-Mills theory away from the origin of the moduli space and demonstrate that the results are extremely simple, in much the same way as in the conformally invariant theory. Specifically, we c