Derivation of the Null Energy Condition
  We derive the null energy condition, understood as a constraint on the Einstein-frame Ricci tensor, from worldsheet string theory. For a closed bosonic string propagating in a curved geometry, the spacetime interpretation of the Virasoro constraint condition is precisely the null energy condition, to leading nontrivial order in the alpha-prime expansion. Thus the deepest origin of the null energy condition lies in worldsheet diffeomorphism invariance. 
Maulik Parikh and Jan Pieter van der Schaar
hep-th astro-ph.CO gr-qc