Non-locality of the C- and D-theories

TL;DR

This paper explores the connection between non-local gravity theories and C-theories, demonstrating that certain C-theories can be mapped to ghost-free nonlocal gravity, potentially aiding in the development of renormalizable gravity models.

Contribution

It establishes an exact mapping between simple C-theories and ghost-free nonlocal gravity, opening new avenues for analyzing infinite-order derivative theories and D-theories.

Findings

Simple C-theories can be mapped to ghost-free nonlocal gravity

This mapping provides a new tool for studying infinite-order derivative theories

Potential implications for renormalizable gravity models

Abstract

Apparent similarities between non-local theories of gravity and the so-called C-theories are pointed out. It is shown that some simple C-theories can be mapped exactly into a previously considered type of ghost-free nonlocal gravity. This may introduce a useful tool to tackle some infinite-order derivative theories and raises the possibility of describing renormalisable gravity in a new context of D-theories.