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

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.