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Register a new userThe local renormalization of super-Yang-Mills theories
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Marc Gillioz
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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.
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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 three renormalization constants are needed, which can be identified with the coupling constant, gauge field and gluino renormalization. The non-renormalization theorem of the gluon-ghost-antighost vertex in the Landau gauge is shown to remain valid in N=1 Super Yang-Mills. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino. These features are explicitly checked through a three loop calculation.
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 parameter. The (anti-)self-dual Landau gauge is recovered at the vanishing of each gauge parameter. The theory shows itself to be renormalizable in these classes of gauges. Moreover, we discuss the ambiguity on the choice of the renormalization factors (which is not present in usual Yang-Mills theories) and argue a possible origin of such ambiguity.
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 rheonomic and superspace actions. The corresponding supergeometry and integration theory are discussed in detail. This formalism is an efficient tool for building supersymmetric models in a geometrical framework.
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 attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the ${cal N} =4$ super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the $ {cal N}=frac12$ theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.
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 consider the model where an SU(2) gauge group is spontaneously broken down to U(1). The complete component Lagrange density of the model is given in a form useful for perturbative calculations. We argue that the scattering amplitudes with massive external states deserve further study. Finally, our work shows that loop corrections can be readily computed in a mass-regulated N=4 theory, which may be relevant in trying to connect weak-coupling results with those at strong coupling, as discussed recently by Alday and Maldacena.
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