Asymptotic safety meets tensor field theory: towards a new class of gravity-matter systems

TL;DR

This paper explores a novel tensor field theory coupled with quantum gravity, demonstrating a potential asymptotically safe fixed point with non-zero scalar coupling in four dimensions, advancing the understanding of gravity-matter interactions.

Contribution

It introduces the first example of a gravity-scalar system in four dimensions exhibiting asymptotic safety with a non-zero scalar quartic coupling, combining tensor field theory with quantum gravity.

Findings

Quantum gravity screens scalar quartic couplings in scalar models.

Tensor field theory with $O(N)^3$ symmetry exhibits an interacting fixed point with gravity.

Matter self-interactions are antiscreening, competing with gravitational screening.

Abstract

Combining asymptotically safe quantum gravity with a tensor field theory, we exhibit the first example of a theory with gravity and scalar fields in four dimensions which may realize asymptotic safety at a non-vanishing value of the scalar quartic coupling. We first present (further) evidence that in the asymptotic-safety paradigm, quantum fluctuations of gravity generically screen the quartic couplings in (multi-)scalar models. For a tensor field theory in which the scalar field transforms under an internal $O(N)^3$ symmetry, this has the effect of replacing asymptotic freedom, recently discovered at large $N$ on a fixed flat background, by an interacting fixed point in the presence of quantum gravity. The fixed point originates from the competition between the effects of the matter self-interactions which, contrary to the usual scalar models, are antiscreening, and the screening gravitational effects.