Spin-2 and the Weak Gravity Conjecture

Understand

Recently, it has been argued that application of the Weak Gravity Conjecture (WGC) to spin-2 fields implies a universal upper bound on the cutoff of the effective theory for a single spin-2 field.

• We point out here that these arguments are largely spurious, because of the absence of states carrying spin-2 Stuckelberg $U(1)$ charge, and because of incorrect scaling assumptions.
• Known examples such as Kaluza-Klein theory that respect the usual WGC do so because of the existence of a genuine $U(1)$ field under which states are charged, as in the case of the Stuckelberg formulation of spin-1 theories, for which there is an unambiguously defined $U(1)$ charge.
• Theories of bigravity naturally satisfy a naive formulation of the WGC, $M_W< M_{\rm Pl}$, since the force of the massless graviton is always weaker than the massive spin-2 modes.