Improved Effective Potential in Curved Spacetime and Quantum Matter - Higher Derivative Gravity Theory

Details Improved Effective Potential in Curved Spacetime and Quantum Matter - Higher Derivative Gravity Theory Improved Effective Potential in Curved Spacetime and Quantum Matter - Higher Derivative Gravity Theory

1994-10-17

arxiv.org/abs/hep-th/9410113v1

Phys.Rev.D51:1680-1691,1995

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, Oct 17 1994

Scientific paper

10.1103/PhysRevD.51.1680

\noindent{\large\bf Abstract.} We develop a general formalism to study the renormalization group (RG) improved effective potential for renormalizable gauge theories ---including matter-$R^2$-gravity--- in curved spacetime. The result is given up to quadratic terms in curvature, and one-loop effective potentials may be easiliy obtained from it. As an example, we consider scalar QED, where dimensional transmutation in curved space and the phase structure of the potential (in particular, curvature-induced phase trnasitions), are discussed. For scalar QED with higher-derivative quantum gravity (QG), we examine the influence of QG on dimensional transmutation and calculate QG corrections to the scalar-to-vector mass ratio. The phase structure of the RG-improved effective potential is also studied in this case, and the values of the induced Newton and cosmological coupling constants at the critical point are estimated. Stability of the running scalar coupling in the Yukawa theory with conformally invariant higher-derivative QG, and in the Standard Model with the same addition, is numerically analyzed. We show that, in these models, QG tends to make the scalar sector less unstable.

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