Derivation of the null energy condition

Abstract

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 ${\ensuremath{\alpha}}^{\ensuremath{'}}$ expansion. Thus the deepest origin of the null energy condition lies in world sheet diffeomorphism invariance.