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

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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Shortened, LaTeX, 2 figures

Scientific paper

10.1016/0550-3213(95)00674-5

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.

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