Renormalization Group Properties of Higher-Derivative Quantum Gravity with Matter in $4-\varepsilon$ Dimensions

TL;DR

This paper explores how higher-derivative quantum gravity influences the phase structure and fixed points of matter theories in 4-ε dimensions, revealing new IR-stable fixed points and their impact on phase transitions.

Contribution

It identifies new fixed points induced by quantum gravity in matter theories and analyzes their implications for phase transitions and effective potentials.

Findings

Discovery of new IR-stable fixed points influenced by quantum gravity.

Quantum gravity induces second-order phase transitions at non-zero temperature.

Shape of the effective potential in SU(2) theory is significantly affected by quantum gravity.

Abstract

We investigate the phase structure and the infrared properties of higher-derivative quantum gravity (QG) with matter, in $4-\varepsilon$ dimensions. The renormalization group (RG) equations in $4-\varepsilon$ dimensions are analysed for the following types of matter: the $f\varphi^4$-theory, the $O(N) \varphi^4$-theory, scalar electrodynamics, and the $SU(2)$ model with scalars. New fixed points for the scalar coupling appear ---one of which is IR stable--- being some of them 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 nonzero temperature and it is shown that its shape is clearly influenced by QG.