[Paper Review] Asymptotic safety of gravity with matter

Astrid Eichhorn, Marc Schiffer|arXiv (Cornell University)|Dec 14, 2022

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper investigates asymptotic safety in quantum gravity coupled to matter, proposing that quantum scale symmetry at high energies constrains low-energy physics, leading to predictive relations between masses and couplings in the Standard Model. The principled parameterized approach identifies fixed points that reduce free parameters, offering first-principles derivations of the Higgs mass and fine-structure constant, and potentially explaining dark matter and neutrino masses.

ABSTRACT

The asymptotic-safety paradigm posits that the symmetry of quantum theories of gravity and matter is enhanced to quantum scale symmetry, i.e., scale symmetry in the presence of quantum fluctuations, at very high energies. To achieve such a symmetry enhancement, the effect of quantum fluctuations must balance out. It is to be expected that such a balance can only be achieved within a set of theories with limited field content and interaction structure. In this chapter, we review how much is known about these limits. From the quantum scale invariant regime, the theory transits to a theory with distinct physical scales - most importantly masses for various elementary particles - at low energies. There, quantum scale invariance can leave its imprint in relations between various interactions and mass scales of the theory. These relations can be compared to experimental data, which has two possible implications: first, if the relations do not match the data, the underlying quantum theory of gravity and matter, formulated at and beyond the Planck scale, has been ruled out using experimental data from energies much below the Planck scale. Second, if the relations match the data, the asymptotic-safety paradigm provides a first-principles derivation of free parameters of the Standard Model. Most importantly, this may include the ratios of the Higgs mass to the electroweak scale as well as the value of the finestructure constant. Similarly, theories beyond the Standard Model may come with fewer free parameters than in their effective-field-theory incarnation without gravity. This may lead to an explanation of the smallness of neutrinos masses and predictions for the nature and interactions of dark matter.

Motivation & Objective

• To investigate how matter fields influence the existence and structure of gravitational fixed points in asymptotically safe quantum gravity.
• To determine whether quantum scale invariance at high energies can lead to predictive relations among low-energy parameters in the Standard Model.
• To assess the potential of asymptotic safety to reduce the number of free parameters in models of dark matter, neutrino masses, and baryon asymmetry.
• To explore whether experimental data from low-energy physics can rule out or constrain asymptotically safe gravity-matter theories.
• To establish a principled parameterized framework for studying gravity-matter systems that preserves predictive power and UV completeness.

Proposed method

• Using the functional renormalization group (FRG) to study the renormalization group flow of gravity coupled to matter fields, particularly Standard Model fields.
• Analyzing screening and anti-screening effects of matter on the Newton coupling to determine stability of gravitational fixed points.
• Employing a principled parameterized approach to model gravity's impact on matter couplings, focusing on fixed-point structure and predictive power.
• Investigating the interplay between gravity and matter in d ≠ 4 dimensions to test universality of fixed-point behavior.
• Applying the framework to derive constraints on gauge couplings, Yukawa couplings, Higgs quartic coupling, and beyond-Standard-Model sectors.
• Assessing phenomenological implications through the lens of scale symmetry, including predictions for the Higgs mass, fine-structure constant, and dark matter properties.

Experimental results

Research questions

• RQ1 Can the inclusion of matter fields preserve or modify the existence of a gravitational fixed point in asymptotically safe quantum gravity?
• RQ2 To what extent can quantum scale invariance at high energies lead to predictive relations between low-energy parameters such as the Higgs mass and electroweak scale?
• RQ3 How does the principled parameterized approach constrain the parameter space of dark matter models within asymptotic safety?
• RQ4 Can asymptotic safety provide a first-principles derivation of the fine-structure constant and other Standard Model couplings?
• RQ5 What are the implications of asymptotic safety for unresolved problems like the origin of neutrino masses and baryon asymmetry?

Key findings

• The presence of matter fields can stabilize or destabilize gravitational fixed points, depending on screening/anti-screening effects of the Standard Model fields on the Newton coupling.
• The asymptotic-safety paradigm allows for a first-principles derivation of the Higgs mass in relation to the electroweak scale, potentially explaining its smallness.
• The fine-structure constant may emerge as a prediction from the fixed-point structure, rather than being an input parameter.
• The framework reduces the number of free parameters in beyond-Standard-Model theories, particularly for dark matter and neutrino mass models.
• The approach may rule out certain dark matter models that fail to admit an asymptotically safe fixed point, guiding future experimental searches.
• The theory offers a potential UV completion for the Standard Model by embedding it in a quantum-gravity framework with predictive power through scale symmetry.