Renormalization group properties of higher-derivative quantum gravity with matter in 4-epsilon dimensions

We investigate the phase structure and the infrared properties of higher-derivative quantum gravity (QG) with matter, in 4 - epsilon dimensions, The renormalization group (RG) equations in 4 - epsilon dimensions are analysed for the following types of matter: the f phi(4) theory, the O(N)phi(4) theory, scalar electrodynamics, and the SU(2) model with scalars. New fixed points for the scalar coupling appear-one of which is IR stable-some of them being induced by QG. The IR stable fixed point perturbed by QG leads to a second-order phase transition for the theory at non-zero temperature. The RG improved effective potential in the SU(2) theory (which can be considered as the confining phase of the standard model) is calculated at non-zero temperature and it is shown that its shape is clearly influenced by QG.