Radiative Corrections in Kaluza-Klein Theories

Abstract

The most direct experimental signature of a compactified extra dimension would be the appearance of an infinite tower of Kaluza-Klein particles. Such modes would be identified by their unique spectrum of masses and couplings, but these properties are subject to radiative corrections. We therefore investigate the extent to which such corrections deform the expected tree-level relations between the Kaluza-Klein masses and couplings, and thereby alter the experimental signatures of Kaluza-Klein modes. However, in order to perform this analysis, it is first necessary to develop several new techniques in quantum field theory which can regularize divergences in Kaluza-Klein theories. Specifically, quantum field theory regulators which respect appropriate higher dimensional symmetries are needed. We therefore develop two new regulators for quantum field theories in spacetimes with compactified extra dimensions. Although based on traditional four-dimensional regulators, the key new feature of these higher-dimensional regulators is that they are specifically designed to handle mixed spacetimes in which some dimensions are infinitely large and others are compactified. Moreover, unlike most other regulators which have been used in the extra-dimension literature, these regulators are designed to respect the original higher-dimensional Lorentz and gauge symmetries that exist prior to compactification, and not merely the four-dimensional symmetries which remain afterward. This distinction is particularly relevant for calculations of the physics of the excited Kaluza-Klein modes themselves, and not merely their radiative effects on zero modes. By respecting the full higher-dimensional symmetries, our regulators avoid the introduction of spurious terms which would not have been easy to disentangle from the physical effects of compactification. We then apply our methods to calculations of Kaluza-Klein spectra in 5D Phi to the Fourth theory and Yukawa theory.