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We consider the possibility that the UV completeness of a fundamental theoryis achieved by a modification of propagators at large momenta. We assume thatgeneral covariance is preserved at all energies, and focus on the coupling of ascalar field to the background geometry as an example. Naively, one expectsthat the gravitational interaction, like Yukawa interactions, will beregularized by a propagator which decays to zero sufficiently fast above somecutoff scale, but we show that in order to avoid the ultra-violet divergence,the propagator should approach to a nonzero constant. This incompatibilitybetween the regularizations of gravitational and Yukawa interactions suggeststhat a symmetry of the particle spectrum is needed for a UV completefundamental theory.Comment: 9 pages, minor modificatio

Regularization of Newton constant, trans-Planckian dispersion relation and symmetry of particle spectrum