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

TL;DR

This paper develops a formalism for the RG-improved effective potential in curved spacetime, incorporating higher-derivative gravity, and explores its implications for phase transitions, mass ratios, and stability in various quantum field theories.

Contribution

It introduces a general method to compute the effective potential in curved spacetime with higher-derivative gravity, including applications to scalar QED and the Standard Model.

Findings

QG influences dimensional transmutation and phase structure.

QG corrections affect scalar-to-vector mass ratios.

Higher-derivative gravity tends to stabilize the scalar sector.

Abstract

\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.