Derivation of the Null Energy Condition

We derive the null energy condition, understood as a constraint on the Einstein-frame Ricci tensor, from world sheet 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 α′ expansion. Thus the deepest origin of the null energy condition lies in world sheet diffeomorphism invariance.