Approaching gravitation by quantum gravity with matter near four dimensions

Abstract

The phase structure and infrared (IR) behavior of higher-derivative quantum gravity (QG) near (but below) four dimensions, with a few different matter theories, shows remarkable properties. Models of this sort can be analyzed by renormalization group (RG) methods in 4 – ε dimensions for the following matter sectors: f ?, 0(N) ?, scalar electrodynamics, and SU(2) with scalars. New fixed points for the scalar coupling are predicted and one of them turns out to be infrared (IR) stable. For the theory at nonzero temperature, the QG-perturbed IR stable fixed point leads then to a second order phase transition. Other noticeable effects of QG influence are changes in the shape of the RG improved effective potential, like in the SU(2)theory, which can be viewed as the confining phase of the standard model.