Nonminimal hints for asymptotic safety

Astrid Eichhorn,Vedran Skrinjar,Stefan Lippoldt

doi:10.1103/physrevd.97.026002

Abstract

In the asymptotic-safety scenario for gravity, nonzero interactions are present in the ultraviolet. This property should also percolate into the matter sector. Symmetry- based arguments suggest that nonminimal derivative interactions of scalars with curvature tensors should therefore be present in the ultraviolet regime. We perform a nonminimal test of the viability of the asymptotic-safety scenario by working in a truncation of the Renormalization Group flow, where we discover the existence of an interacting fixed point for a corresponding nonminimal coupling. The back-coupling of such nonminimal interactions could in turn destroy the asymptotically safe fixed point in the gravity sector. As a key finding, we observe nontrivial indications of stability of the fixed-point properties under the impact of nonminimal derivative interactions, further strengthening the case for asymptotic safety in gravity-matter systems.

Highlights

The quantum-field theory framework has been successfully used in particle physics, various condensed-matter systems, and even to describe the seeds for structure formation in the early Universe
In line with expectations based on symmetry arguments [32], we have confirmed that an asymptotically safe regime in gravity is incompatible with a free matter model
The general structure of the tentative gravity-matter fixed point for standard model matter coupled to gravity is that of a hybrid fixed point: it is free in interactions that break some of the global symmetries of the kinetic terms

Summary

INTRODUCTION

The quantum-field theory framework has been successfully used in particle physics, various condensed-matter systems, and even to describe the seeds for structure formation in the early Universe. Similar to pure-gravity studies, results in gravity-matter models suggest that canonical dimensionality of couplings remains a good guiding principle to determine which couplings are likely to become relevant, i.e., UV attractive, at the asymptotically safe fixed point; see, e.g., [29,30,31]. While they are expected not to feature a fixed point at vanishing coupling, they are not guaranteed to feature a fixed point at a real value of the coupling at all It was conjectured [32] that the interactions compatible with the global symmetries of the kinetic terms of matter fields cannot become asymptotically free when quantum gravity is present. A large backreaction onto the fixed-point value in the gravity sector would constitute a sign of possible instabilities of typically used truncations

FUNCTIONAL RENORMALIZATION GROUP SETUP

Shifted Gaussian fixed point for the nonminimal coupling

Distinction of different avatars of the Newton coupling

2.51 Á Á Á 2 Á Á Á 0 0

Findings

CONCLUSIONS AND OUTLOOK