On Padmanabhan's duality invariance and the quantum of length

Abstract

We provide a field-theoretic construction of Padmanabhan's duality-invariant Feynman propagator for a massive point particle in Euclidean space ${\mathbb{R}}^D$. Padmanabhan's propagator includes quantum-gravity effects due to the existence of a quantum of length $\ell$. Including $O({\ell }^2)$ corrections, the corresponding field-theory model turns out to be a free, massive scalar defined in ${\mathbb{R}}^{D+2}$. The two additional dimensions with respect to the original ${\mathbb{R}}^D$ provide the necessary room, so to speak, for quantum-gravity fluctuations.

14 pages