Renormalized Kaluza-Klein theories

Using six-dimensional quantum electrodynamics ($QED_6$) as an example we study the one-loop renormalization of the theory both from the six and four-dimensional points of view. Our main conclusion is that the properly renormalized four dimensional theory never forgets its higher dimensional origin. In particular, the coefficients of the neccessary extra counterterms in the four dimensional theory are determined in a precise way. We check our results by studying the reduction of $QED_4$ on a two-torus.

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