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

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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 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.
10 pages, Latex

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