On the number of relevant operators in asymptotically safe gravity

TL;DR

This paper discusses the asymptotic safety scenario in quantum gravity, demonstrating that if a non-trivial ultraviolet fixed point exists, then the number of relevant operators is necessarily finite, supporting the theory's consistency.

Contribution

It shows that the finiteness of relevant directions in asymptotically safe gravity follows from the existence of a non-trivial fixed point within the f(R) approximation.

Findings

Finite relevant operators are a consequence of the fixed point structure.

The existence of a non-trivial fixed point implies a finite number of free parameters.

Results support the asymptotic safety scenario for gravity.

Abstract

The asymptotic safety scenario of gravity conjectures that (i) the quantum field theory of gravity exists thanks to the presence of a non-trivial ultraviolet fixed point of the renormalization group, and that (ii) the fixed point has only a finite number of relevant perturbations, i.e. a finite number of UV-stable directions (or in other words, a finite number of free parameters to be fixed experimentally). Within the f(R) approximation of the functional renormalization group equation of gravity, we show that assuming the first half of the conjecture to be true, the remaining half follows from general arguments, that is, we show that assuming the existence of a non-trivial fixed point, the fact that the number of relevant directions is finite is a general consequence of the structure of the equations.