Renormalization group properties of higher-derivative quantum gravity with matter in 4 - ε dimensions Original Research Article

We investigate the phase structure and the infrared properties of higher-derivative quantum gravity (QG) with matter, in 4 - ε dimensions. The renormalization group (RG) equations in 4 - ε dimensions are analysed for the following types of matter: the fϕ4 theory, the O(N)ϕ4 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.