# Reflection positivity in nonlocal gravity

## TL;DR

This paper demonstrates that nonlocal field theories, including weakly nonlocal gravity and gauge theories, satisfy a simple test for reflection positivity, countering recent claims to the contrary.

## Contribution

It introduces and applies a simple perturbative reflection positivity test to nonlocal theories, showing they satisfy this property in the coincidence limit.

## Key findings

- Nonlocal field theories satisfy the perturbative reflection positivity test.
- Weakly nonlocal gravity and gauge theories pass the test.
- Counterexamples to recent claims are provided.

## Abstract

Contrary to recent claims in the literature, a simple test for reflection positivite, which we call perturbative reflection positivity in the coincidence limit, is shown to be satisfied for nonlocal field theories. Particular attention is given to weakly nonlocal gravity and gauge theories.