The Gravitino and the Swampland
  We propose a new swampland conjecture stating that the limit of vanishing
gravitino mass corresponds to the massless limit of an infinite tower of states
and to the consequent breakdown of the effective field theory. We test our
proposal in large classes of models coming from compactification of string
theory to four dimensions, where we identify the Kaluza-Klein nature of the
tower of states becoming light. We point out a general relation between the
gravitino mass and abelian gauge coupling in models with extended
supersymmetry, which can survive also in examples with minimal supersymmetry.
This allows us to connect our conjecture to other well established swampland
conjectures, such as the weak gravity conjecture or the absence of global
symmetries in quantum gravity. We discuss phenomenological implications of our
conjecture in (quasi-)de Sitter backgrounds and extract a lower bound for the
gravitino mass in terms of the Hubble parameter.
