Massive Higher-Spin Multiplets and Asymptotic Freedom in Quantum Gravity

TL;DR

This paper investigates how massive higher-spin fields, when coupled to quantum gravity and treated with the fakeon prescription, can lead to asymptotic freedom, revealing specific field configurations that achieve this property.

Contribution

It introduces a novel analysis of higher-spin multiplets in quantum gravity using the fakeon prescription, identifying conditions for asymptotic freedom in these theories.

Findings

Only certain numbers of irreducible rank-s bosons with s ≤ 3 are compatible with asymptotic freedom.

No solutions involving fermionic rank-s fields were found.

Nonminimal kinetic terms for rank-1 and symmetric rank-2 tensors enlarge the allowed field configurations.

Abstract

We consider massive higher-spin multiplets coupled to quantum gravity and compute their contributions to the gravitational beta functions at one loop. Such theories, if quantized with the Feynman prescription, would contain ghosts. Instead, those degrees of freedom are turned into purely virtual particles by means of the fakeon prescription and the resulting theories are both renormalizable and unitary. We extract the necessary number of fields to obtain asymptotic freedom by solving the relevant renormalization-group equations in the ultraviolet limit. We show that in the case of irreducible rank-$s$ bosons with minimal kinetic term only a certain number of fields with $0\leq s \leq 3$ is compatible with asymptotic freedom. No solution involving fermionic rank-$s$ fields are found. We also consider the cases of rank-$1$ and symmetric rank-$2$ tensor fields with nonminimal kinetic terms and repeat the analysis, finding that the allowed number of fields is enlarged. Possible implications for metric affine theories of gravity are pointed out.