Quantum Gravity Constraints from Unitarity and Analyticity

TL;DR

This paper establishes rigorous positivity bounds on higher-curvature corrections to Einstein gravity using unitarity and analyticity, constraining effective theories and string models in various dimensions.

Contribution

It systematically derives and enumerates positivity bounds on curvature operators in multiple dimensions, including supersymmetric cases, and relates these bounds to string theory consistency.

Findings

Positivity bounds require certain curvature operators to have positive coefficients.

The Gauss-Bonnet term in D≥5 is inconsistent without new degrees of freedom.

All bounds are satisfied by weakly-coupled string theories.

Abstract

We derive rigorous bounds on corrections to Einstein gravity using unitarity and analyticity of graviton scattering amplitudes. In $D\geq 4$ spacetime dimensions, these consistency conditions mandate positive coefficients for certain quartic curvature operators. We systematically enumerate all such positivity bounds in $D=4$ and $D=5$ before extending to $D\geq 6$. Afterwards, we derive positivity bounds for supersymmetric operators and verify that all of our constraints are satisfied by weakly-coupled string theories. Among quadratic curvature operators, we find that the Gauss-Bonnet term in $D\geq 5$ is inconsistent unless new degrees of freedom enter at the natural cutoff scale defined by the effective theory. Our bounds apply to perturbative ultraviolet completions of gravity.