Derivation of the Null Energy Condition

TL;DR

This paper derives the null energy condition from worldsheet string theory, showing it originates from fundamental string symmetries and providing a deep theoretical foundation for this energy constraint.

Contribution

It establishes a direct derivation of the null energy condition from string theory principles, linking spacetime energy conditions to worldsheet diffeomorphism invariance.

Findings

Null energy condition derived from string theory

Spacetime interpretation of Virasoro constraints

Null energy condition rooted in worldsheet symmetry

Abstract

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.