Quantum gravity at a large number of dimensions

TL;DR

This paper explores the large-$D$ limit of Einstein gravity, showing that a consistent dominant class of planar diagrams exists and that the effective field theory extension remains well-defined and renormalizable at high energies.

Contribution

It demonstrates that the large-$D$ limit in Einstein gravity is dominated by a specific subclass of planar diagrams, and that the effective field theory extension preserves this limit, leading to a renormalizable quantum gravity theory.

Findings

Large-$D$ graph limit exists and is dominated by planar diagrams.

Effective field theory extension does not alter the dominant large-$D$ graph subclass.

The resulting theory is renormalizable up to the Planck scale.

Abstract

We consider the large-$D$ limit of Einstein gravity. It is observed that a consistent leading large-$D$ graph limit exists, and that it is built up by a subclass of planar diagrams. The graphs in the effective field theory extension of Einstein gravity are investigated in the same context, and it is seen that an effective field theory extension of the basic Einstein-Hilbert theory will not upset the latter leading large-$D$ graph limit, {\it i.e.}, the same subclass of planar diagrams will dominate at large-$D$ in the effective field theory. The effective field theory description of large-$D$ quantum gravity limit will be renormalizable, and the resulting theory will thus be completely well defined up to the Planck scale at $\sim 10^{19}$ GeV. The $(\frac1D)$ expansion in gravity is compared to the successful $(\frac1N)$ expansion in gauge theory (the planar diagram limit), and dissimilarities and parallels of the two expansions are discussed. We consider the expansion of the effective field theory terms and we make some remarks on explicit calculations of $n$-point functions.