The averaged null energy condition for general quantum field theories in two dimensions

It is shown that the averaged null energy condition is fulfilled for a dense, translationally invariant set of vector states in any local quantum field theory in two-dimensional Minkowski spacetime whenever the theory has a mass gap and possesses an energy-momentum tensor. The latter is assumed to be a Wightman field which is local relative to the observables, generates locally the translations, is divergence-free, and energetically bounded. Thus the averaged null energy condition can be deduced from completely generic, standard assumptions for general quantum field theory in two-dimensional flat spacetime.