Weak Gravity Conjecture for the Effective Field Theories with N Species

Abstract

We conjecture an intrinsic UV cutoff for the validity of the effective field theory with a large number of species coupled to gravity. In four dimensions such a UV cutoff takes the form $\Lambda=\sqrt{\lambda/ N}M_p$ for $N$ scalar fields with the same potential $\lambda \phi_i^4$, $i=1,...,N$. This conjecture implies that the assisted chaotic inflation or N-flation might be in the swampland, not in the landscape. Similarly a UV cutoff $\Lambda=gM_p/\sqrt{N}$ is conjectured for the U(1) gauge theory with $N$ species.