Fermions and the Swampland

TL;DR

This paper explores Swampland constraints related to fermions, proposing that fermions must couple to an infinite tower of states with a mass scale linked to Yukawa couplings, and discusses implications for supersymmetry breaking.

Contribution

It introduces a fermionic version of the Weak Gravity Conjecture, connecting fermion couplings to an infinite tower of states and supersymmetry breaking scales.

Findings

Fermions must couple to an infinite tower of states.

The mass scale of the tower is set by Yukawa couplings.

Supersymmetry breaking occurs below the Yukawa scale.

Abstract

In this note we consider whether there could be Swampland constraints associated to the presence of fermions in the theory. We propose that any fermion must couple to an infinite tower of states, and that the mass scale of this tower, in Planck units, is set by the strength of the Yukawa coupling to the tower. This is a type of fermionic version of the (magnetic) Weak Gravity Conjecture. We also find that supersymmetry plays a natural part in this fermionic realisation, which motivates a further proposal that supersymmetry can only be broken below the scale set by this Yukawa coupling. We perform some preliminary checks in string theory of these ideas.