Absence of a charge renormalization in the Higgs model interacting with conformal two-dimen.pdfVIP

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Absence of a charge renormalization in the Higgs model interacting with conformal two-dimen.pdf

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Absence of a charge renormalization in the Higgs model interacting with conformal two-dimen

a r X i v : h e p - t h / 0 2 0 3 1 9 6 v 1 2 1 M a r 2 0 0 2 Absence of a charge renormalization in the Higgs model interacting with conformal two-dimensional gravity Z. Haba Institute of Theoretical Physics, University of Wroclaw, 50-204 Wroclaw, Plac Maxa Borna 9,Poland e-mail:zhab@ift.uni.wroc.pl Abstract We discuss D-dimensional scalar and electromagnetic fields interacting with a quantized metric. The gravitons depend solely on twodimensional coordinates. We consider a conformal field theory as a model for the metric tensor.We show that an interaction with gravity improves the short distance behaviour. As a result there is no charge renormalization in the fourdimensional Higgs model. 1 Introduction We discuss D-dimensional scalar and electromagnetic fields interacting with a quantized scale invariant metric. The gravitons depend only on twodimensional coordinates. These coordinates could be considered either as additional coordi- nates (e.g., in the brane picture when gravitons can escape to extra dimensions [1]) or as a (stringy) perturbation of the physical fourdimensional space-time deforming the flat Minkowski metric. In our earlier paper [2] we have shown that as a result of an interaction with a scale invariant quantum gravity the propagators of quantum matter fields become more regular than the ones in a classical gravitational field. In this paper we consider a specific model of a scale invariant quantum metric. We show that as a result of an interaction with a conformal invariant twodimensional gravity the fourdimensional Higgs model has no charge renormalization. This property can still hold true in five dimensions depending on the scale dimension of the twodimensional gravity. Higher dimensional models can still be renormalizable if we can treat properly more singular gravitational fields. We also show that after an interaction with twodimensional gravity the standard dispersion relation 1 (relating the temporal component of the wave vector to