Regularization of Newton Constant, Trans-Planckian Dispersion Relation, and Symmetry of Particle Spectrum

TL;DR

This paper explores how modifying propagators at high energies can achieve UV completeness in a gravitational context, revealing the need for particle spectrum symmetry to avoid divergences.

Contribution

It demonstrates that regularizing gravitational interactions requires a nonzero propagator at high momenta, implying the necessity of particle spectrum symmetry for UV completion.

Findings

Propagators must approach a nonzero constant at high momenta.

Regularization of gravity differs from Yukawa interactions.

Symmetry of particle spectrum is essential for UV completeness.

Abstract

We consider the possibility that the UV completeness of a fundamental theory is achieved by a modification of propagators at large momenta. We assume that general covariance is preserved at all energies, and focus on the coupling of a scalar field to the background geometry as an example. Naively, one expects that the gravitational interaction, like Yukawa interactions, will be regularized by a propagator which decays to zero sufficiently fast above some cutoff scale, but we show that in order to avoid the ultra-violet divergence, the propagator should approach to a nonzero constant. This incompatibility between the regularizations of gravitational and Yukawa interactions suggests that a symmetry of the particle spectrum is needed for a UV complete fundamental theory.