Renormalization Group Flow in Scalar-Tensor Theories. II

TL;DR

This paper investigates the ultraviolet behavior of scalar-tensor theories with higher powers of scalar curvature and fields using Functional Renormalization Group methods, identifying fixed points and analyzing their properties across dimensions.

Contribution

It demonstrates the existence of UV fixed points with non-trivial gravitational couplings and Gaussian matter couplings, and establishes recursive relations among critical exponents in these theories.

Findings

UV fixed points with non-trivial gravitational couplings

Recursive relations among critical exponents

UV critical surface is five dimensional in studied models

Abstract

We study the UV behaviour of actions including integer powers of scalar curvature and even powers of scalar fields with Functional Renormalization Group techniques. We find UV fixed points where the gravitational couplings have non-trivial values while the matter ones are Gaussian. We prove several properties of the linearized flow at such a fixed point in arbitrary dimensions in the one-loop approximation and find recursive relations among the critical exponents. We illustrate these results in explicit calculations in $d=4$ for actions including up to four powers of scalar curvature and two powers of the scalar field. In this setting we notice that the same recursive properties among the critical exponents, which were proven at one-loop order, still hold, in such a way that the UV critical surface is found to be five dimensional. We then search for the same type of fixed point in a scalar theory with minimal coupling to gravity in $d=4$ including up to eight powers of scalar curvature. Assuming that the recursive properties of the critical exponents still hold, one would conclude that the UV critical surface of these theories is five dimensional.