Quantum field theories of arbitrary-spin massive multiplets and Palatini quantum gravity

TL;DR

This paper develops quantum field theories for arbitrary-spin massive multiplets incorporating fake particles, enabling consistent, renormalizable, and unitary models that can couple to quantum gravity and gauge fields.

Contribution

It introduces a novel formulation of quantum field theories with fake particles for arbitrary spins, ensuring locality, unitarity, and renormalizability simultaneously.

Findings

Theories admit cubic and quartic self-interactions.

Mass spectra are constrained by RG invariant relations.

Palatini quantum gravity with fakeons is equivalent to non-Palatini form.

Abstract

We formulate quantum field theories of massive fields of arbitrary spins. The presence of both physical and fake particles, organized into multiplets, makes it possible to fulfill the requirements of locality, unitarity and renormalizability at the same time. The theories admit cubic and quartic self-interactions and can be coupled to quantum gravity and gauge fields. The simplest irreducible bosonic and fermionic multiplets are made of towers of alternating physical and fake particles. Their mass spectrum is constrained by RG invariant relations and depends on just one or two masses. The fixed points of the renormalization-group flow are scale invariant, but not necessarily conformal invariant. The Palatini version of quantum gravity with fakeons is equivalent to the non-Palatini one coupled to a peculiar multiplet of order 3. As a consequence, it is equally renormalizable and unitary.