Positivity of Curvature-Squared Corrections in Gravity

TL;DR

This paper proves that in higher-dimensional gravity theories with certain UV completions, the Gauss-Bonnet correction term must have a nonnegative coefficient, ensuring consistency with unitarity and absence of ghosts.

Contribution

It provides a rigorous proof that the Gauss-Bonnet term's coefficient is nonnegative in dimensions greater than four under specific UV completion assumptions.

Findings

Gauss-Bonnet coefficient is nonnegative in >4 dimensions

Proof relies on unitarity of spectral representation

Assumes ghost- and tachyon-free UV completion

Abstract

We study the Gauss-Bonnet (GB) term as the leading higher-curvature correction to pure Einstein gravity. Assuming a tree-level ultraviolet completion free of ghosts or tachyons, we prove that the GB term has a nonnegative coefficient in dimensions greater than four. Our result follows from unitarity of the spectral representation for a general ultraviolet completion of the GB term.