Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory

TL;DR

This paper explores the ultraviolet completion of an $O(N)$ scalar theory coupled to gravity, demonstrating a mechanism for asymptotic safety with a flat potential at high energies using the Wilsonian RG approach.

Contribution

It identifies a new fixed point in the RG flow that ensures asymptotic safety and constrains infrared couplings in the scalar-gravity system.

Findings

Discovery of a UV-attractive fixed point with vanishing quartic coupling.

RG trajectories remain regular and approach the fixed point.

The mechanism is robust under different cutoff schemes and truncations.

Abstract

We investigate the ultraviolet completion of an $O(N)$ scalar field theory non-minimally coupled to gravity using the Wilsonian functional renormalization group in the proper-time formulation. Focusing on the spontaneously broken phase, we study the RG flow of the scalar potential and the non-minimal curvature coupling expanded around a running minimum. We identify two distinct classes of fixed-point solutions, one of which is ultraviolet attractive and characterized by a vanishing quartic coupling together with finite, interacting gravitational couplings. For a finite region of infrared initial conditions, the RG trajectories remain regular at all scales and approach this fixed point. This mechanism renders the theory asymptotically safe and leads to a flat scalar potential in the ultraviolet. We show that this mechanism is robust under changes of cutoff scheme and truncation, allowing the ultraviolet completion requirement to constrain the infrared values of the scalar couplings and the mass scale in the broken phase.