A Spin-2 Conjecture on the Swampland

TL;DR

The paper proposes a Spin-2 Swampland Conjecture: any EFT with Einstein gravity plus a massive spin-2 field of mass m, and an interaction scale M_w, must have a universal cutoff Λ_m ∼ (m M_p)/M_w, signaling an infinite tower of states. This bound is motivated by applying the Weak Gravity Conjecture to the Stückelberg field and is supported by analyses of bi-gravity (linking to Weyl-squared higher-derivative terms) and string-theory realizations that naturally produce spin-2 towers. The work also discusses the Species scale as an auxiliary bound and explores connections to de Sitter space, culminating in a stronger version of the conjecture for massive gravitons, Λ_m ∼ m. Overall, the conjecture provides a quantum-gravity obstruction to taking the massless limit and has implications for massive gravity, higher-spin theories, and swampland criteria in cosmology.

Abstract

We consider effective theories with massive fields that have spins larger than or equal to two. We conjecture a universal cutoff scale on any such theory that depends on the lightest mass of such fields. This cutoff corresponds to the mass scale of an infinite tower of states, signalling the breakdown of the effective theory. The cutoff can be understood as the Weak Gravity Conjecture applied to the Stückelberg gauge field in the mass term of the high spin fields. A strong version of our conjecture applies even if the graviton itself is massive, so to massive gravity. We provide further evidence for the conjecture from string theory.