Elisabeth Kraus

Renormalization of the minimal supersymmetric standard model

The renormalization of the Minimal Supersymmetric Standard Model is discussed. In particular we focus on the soft-supersymmetry breaking sector of the MSSM and comment on non-renormalization theorems.

Renormalization of the Electroweak Standard Model to All Orders

Abstract We give the renormalization of the standard model of electroweak interactions to all orders of perturbation theory by using the method of algebraic renormalization, which is based on general properties of renormalized perturbation theory and not on a specific regularization scheme. The Green functions of the standard model are uniquely constructed to all orders, if one defines the model by the Slavnov–Taylor identity, Ward identities of rigid symmetry, and the specific form of the abelian local gauge Ward identity. Special attention is directed to the mass diagonalization of massless and massive neutral vectors and ghosts. For obtaining off-shell infrared finite expressions it is required to take into account higher order corrections into the functional symmetry operators. It is shown that the normalization conditions of the on-shell schemes are in agreement with the most general symmetry transformations allowed by the algebraic constraints.

Renormalization and symmetry conditions in supersymmetric QED

Abstract. For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic renormalization. For practical calculations, a non-invariant regularization scheme may be used together with counterterms from all power-counting renormalizable interactions. From the Slavnov–Taylor identity, expressing gauge invariance, supersymmetry and translational invariance, simple symmetry conditions are derived that are important in a twofold respect: they establish exact relations between physical quantities that are valid to all orders, and they provide a powerful tool for the practical determination of the counterterms. We perform concrete one-loop calculations in dimensional regularization, where supersymmetry is spoiled at the regularized level, and show how the counterterms necessary to restore supersymmetry can be read off easily. In addition, a specific example is given how the supersymmetry transformations in one-loop order are modified by non-local terms.

Non-commutative Lorentz symmetry and the origin of the Seiberg–Witten map

Abstract. We show that the non-commutative Yang–Mills field forms an irreducible representation of the (undeformed) Lie algebra of rigid translations, rotations and dilatations. The non-commutative Yang–Mills action is invariant under combined conformal transformations of the Yang–Mills field and of the non-commutativity parameter

Conformal transformation properties of the energy-momentum tensor in four dimensions

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Renormalization of supersymmetric Yang-Mills theories with soft supersymmetry breaking

. The Seiberg–Witten differential equation results from a covariant splitting of the combined conformal transformations and can be computed as the missing piece to complete a covariant conformal transformation to an invariance of the action.

An anomalous breaking of supersymmetry in supersymmetric gauge theories with local coupling

Abstract We study the behaviour of Green functions of the energy-momentum tensor under transformations of the conformal group. For the massless ϕ 4 4 -theory it is shown of dilatations. choice of the improvement parameter are all anomalies expressible by those of dilatations. Otherwise a genuine conformal breaking is also present.

Calculating the anomalous supersymmetry breaking in super Yang-Mills theories with local coupling

Abstract The renormalization of supersymmetric Yang-Mills theories with soft supersymmetry breaking is presented using spurion fields for introducing the breaking terms. It is proven that renormalization of the fields and parameters in the classical action yields precisely the correct counterterms to cancel all divergences. In the course of the construction of higher orders additional independent parameters appear, but they can be shown to be irrelevant in physics respects. Thus, the only parameters with influence on physical amplitudes are the supersymmetric and the well-known soft breaking parameters.

Local couplings, double insertions and the Weyl consistency condition

Abstract We extend the gauge coupling of super-Yang–Mills theories to an external real superfield composed out of a chiral and an antichiral superfield and perform renormalization in the extended model. In one-loop order we find an anomalous breaking of supersymmetry which vanishes in the limit to constant coupling. The anomaly arises from nonlocal contributions and its coefficient is gauge and scheme independent and strictly of one-loop order. In the perturbative framework of the construction the anomaly cannot be absorbed as a counterterm to the classical action. With local gauge coupling the symmetric counterterms with chiral integration are holomorphic functions and this property is independent from the specific regularization scheme. Thus, the symmetric counterterm to the Yang–Mills part is of one-loop order only—and it is the anomaly which gives rise to the two-loop order of the gauge β-function in pure super-Yang–Mills theories and to its closed all-order expression.

Non-renormalization theorems without supergraphs: the Wess–Zumino model

Supersymmetric Yang-Mills-theories with local gauge coupling have a new type of anomalous breaking, which appears as a breaking of supersymmetry in the Wess-Zumino-gauge. The anomalous breaking generates the two-loop order of the gauge