[Paper Review] The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models

Gustavo P. de Brito, Astrid Eichhorn+1 more|arXiv (Cornell University)|Jul 8, 2021

Cosmology and Gravitation TheoriesPhysics and Astronomy227 references32 citations

TL;DR

This paper identifies a weak-gravity bound in asymptotically safe gravity-scalar systems, showing that quantum gravitational fluctuations can drive higher-order scalar couplings to complex fixed points when gravity becomes too strong, rendering asymptotic safety impossible without additional spinning matter. The inclusion of fermions or vectors restores asymptotic safety by suppressing effective gravity strength, explaining why viable matter sectors require spin-1/2 and spin-1 fields beyond scalars.

ABSTRACT

We discover a weak-gravity bound in scalar-gravity systems in the asymptotic-safety paradigm. The weak-gravity bound arises in these systems under the approximations we make, when gravitational fluctuations exceed a critical strength. Beyond this critical strength, gravitational fluctuations can generate complex fixed-point values in higher-order scalar interactions. Asymptotic safety can thus only be realized at sufficiently weak gravitational interactions. We find that within truncations of the matter-gravity dynamics, the fixed point lies beyond the critical strength, unless spinning matter, i.e., fermions and vectors, is also included in the model.

Motivation & Objective

• To investigate whether gravity-scalar systems can achieve asymptotic safety under the functional renormalization group (FRG) framework.
• To determine whether quantum gravitational fluctuations can destabilize scalar interactions by generating complex fixed points.
• To explore whether the inclusion of spinning matter (fermions/vectors) restores asymptotic safety in gravity-matter systems.
• To establish a critical bound on the number of scalar fields beyond which asymptotic safety fails without fermionic or vector contributions.
• To assess the implications for the Standard Model’s matter content in the context of asymptotic safety.

Proposed method

• Employing the functional renormalization group (FRG) with a background field method and a generalized regulator function to compute flow equations.
• Using a truncation that includes gravity, scalar fields, and shift-symmetric interactions, with a focus on the Einstein-Hilbert action and scalar self-couplings.
• Applying a perturbative expansion in the coupling space (PF expansion) to compute beta functions for gravitational and scalar couplings.
• Analyzing the fixed-point structure of the system, particularly the reality of the fixed-point values in the complex plane.
• Evaluating the effective strength of gravitational fluctuations as a function of the number of scalar, fermion, and vector fields.
• Comparing the impact of scalar versus spinning matter on the critical gravity strength via the weak-gravity bound.

Experimental results

Research questions

• RQ1 Does the inclusion of scalar fields alone in a gravity-matter system allow for asymptotic safety under the FRG approach?
• RQ2 At what critical strength of gravitational fluctuations do scalar interactions develop complex fixed-point values, indicating a breakdown of asymptotic safety?
• RQ3 Can the addition of fermions or vector fields restore asymptotic safety by suppressing the effective strength of quantum gravity fluctuations?
• RQ4 What is the upper bound on the number of scalar fields beyond which asymptotic safety fails in the absence of spinning matter?
• RQ5 How do induced matter couplings (e.g., via tadpole diagrams) affect the critical exponent of the Higgs quartic coupling in the presence of gravity?

Key findings

• A weak-gravity bound emerges in scalar-gravity systems when gravitational fluctuations exceed a critical strength, leading to complex fixed-point values in higher-order scalar couplings.
• In the absence of spinning matter, the fixed point lies off the real axis in the complex plane, signaling a breakdown of asymptotic safety for gravity-scalar systems.
• The inclusion of fermions or vector fields reduces the effective strength of quantum gravity fluctuations, allowing the fixed point to remain real and thus preserving asymptotic safety.
• The critical number of scalar fields beyond which asymptotic safety fails without spinning matter is estimated for the first time in this work.
• The indirect gravitational contribution from matter tadpole diagrams (ηmatter_φ) is subleading compared to the direct gravitational contribution in the critical exponent of the Higgs quartic coupling, preserving the irrelevance of λ at the fixed point.
• For the Yukawa coupling, the matter contribution is small but non-negligible, slightly enlarging the viable parameter space for a non-Gaussian fixed point, though still insufficient to restore asymptotic safety without spinning fields.