A Four-Dimensional Theory for Quantum Gravity with Conformal and Nonconformal Explicit Solutions

TL;DR

This paper develops a four-dimensional quantum gravity theory with higher derivatives, identifying explicit conformal and nonconformal solutions, analyzing their finiteness, stability, and potential physical applications.

Contribution

It introduces a comprehensive renormalizable scalar field model in curved spacetime with explicit solutions, advancing understanding of quantum gravity and conformal invariance.

Findings

Identified three conformal and three nonconformal finite solutions

Demonstrated absence of conformal anomaly in finite solutions

Analyzed stability and renormalization group flows of solutions

Abstract

The most general version of a renormalizable $d=4$ theory corresponding to a dimensionless higher-derivative scalar field model in curved spacetime is explored. The classical action of the theory contains $12$ independent functions, which are the generalized coupling constants of the theory. We calculate the one-loop beta functions and then consider the conditions for finiteness. The set of exact solutions of power type is proven to consist of precisely three conformal and three nonconformal solutions, given by remarkably simple (albeit nontrivial) functions that we obtain explicitly. The finiteness of the conformal theory indicates the absence of a conformal anomaly in the finite sector. The stability of the finite solutions is investigated and the possibility of renormalization group flows is discussed as well as several physical applications.