A model of composite gravity with Pauli-Villars regulators

TL;DR

This paper demonstrates that a composite graviton emerges in a scalar field model with a reparametrization invariant action, and confirms its robustness using Pauli-Villars regularization instead of dimensional regularization.

Contribution

The study shows that the emergence of a massless composite graviton is independent of the regularization scheme, confirming its physical robustness in the model.

Findings

Composite graviton appears with Pauli-Villars regularization.

Planck mass depends on Pauli-Villars regulator parameters.

Fine-tuning is necessary for the graviton to emerge.

Abstract

We revisit a model of composite gravity, in the form of a reparametrization invariant, non-polynomial, metric-independent action for scalar fields. Previously, the emergence of a composite massless spin 2 particle, the graviton, was demonstrated by analyzing a two-into-two scalar scattering amplitude. Working in the limit of a large number of physical scalars and using dimensional regularization, it was shown that the scattering amplitude had a pole corresponding to a graviton exchange, provided that a certain fine-tuning was implemented; the Planck mass was determined as a function of the dimensional regularization parameter and a mass scale. Here we demonstrate that the presence of the composite graviton is a robust feature of this model and not an artefact of the choice of regulator, by replacing dimensional regularization with Pauli-Villars fields. The presence of the massless graviton is conditioned by a similar fine-tuning as before. This is arguably a more physical regularization, since the Planck mass now depends on the specifics of the Pauli-Villars regulator fields, e.g. their mass as well as their multiplicity.