Finite Quantum Gravity Amplitudes: No Strings Attached

Abstract

We study the gravity-mediated scattering of scalar fields based on a parameterization of the Lorentzian quantum effective action. We demonstrate that the interplay of infinite towers of spin zero and spin two poles at imaginary squared momentum leads to scattering amplitudes that are compatible with unitarity bounds, causal, and scale-free at trans-Planckian energy. Our construction avoids introducing nonlocalities or the massive higher-spin particles that are characteristic in string theory.

Towards Black-Hole Singularity-Resolution in the Lorentzian Gravitational Path Integral

“…(i) To dynamically suppress singular black-hole spacetimes that are vacuum solutions of Einstein equations, a local action constructed from higher powers of R or R µν alone is insufficient and invariants built out of the Riemann tensor are required. In turn, a local action containing these further invariants may feature ghosts These could be avoided by including appropriate functions of the curvature invariants [83,84] or might be present, but not result in a physical inconsistency of the theory [18,19]. which would be absent if one would restrict to higher powers in R, only.…”

Graviton-mediated scattering amplitudes from the quantum effective action

“…In [45] this question was answered in the affirmative. The physics ingredient underlying such models is an infinite tower of massless (Lee-Wick type) poles located on the imaginary axis of the complex s-plane which exhibits a Regge-type scaling behaviour asymptotically.…”

“…This leads to a specific model where the amplitudes become scale-free and compatible with all fundamental requirements without introducing new particle resonances. This model is described in detail in [45].…”

“…In [45], summarised in section 5.5, we discuss a realisation of a model where this requirement is explicitly met.…”

“…Finally, we reviewed the model introduced in [45], exhibiting scattering amplitudes which are bounded everywhere and scale-free in the UV without introducing new massive degrees of freedom or ghosts. The taming of the UV behaviour is generated by the collective interplay of an infinite tower of massless (Lee-Wick type) poles in the propagator and suitable form factors in the matter sector.…”