Spectral Constraints on Theories of Colored Particles and Gravity

TL;DR

This paper derives strict constraints on the spectrum of theories with light colored particles coupled to gravity, showing that symmetry representations in the UV are limited by crossing symmetry and sum rules, with implications for the nature of the graviton.

Contribution

It introduces a novel approach combining crossing symmetry and sum rules to constrain UV spectra in gravitational theories with colored particles, highlighting the unique role of gravity.

Findings

UV states must satisfy specific symmetry irrep conditions

Massless spin-2 must be a singlet under the symmetry group

Gravity imposes constraints absent in non-gravitational theories

Abstract

In this letter, we consider effective field theories for light fields transforming under the fundamental or adjoint representation of a continuous group. We demonstrate that in the presence of gravity, crossing symmetry combined with two subtraction sum rules, leads to stringent constraints on the spectrum of its ultraviolet (UV) completion. Such constraints come in the form of necessary conditions on the symmetry group irreps of the UV states. This is in sharp contrast with non-gravitational theories where anything goes. Beautifully, the graviton pole is the anchor of our argument, not an obstruction. Using numerical methods, we also demonstrate that the massless spin-2 must be a singlet under said symmetry group.