Curious QNEIs from QNEC: New Bounds on Null Energy in Quantum Field Theory

We derive new families of quantum null energy inequalities (QNEIs), i.e. bounds on integrated null energy, in quantum field theories in two and higher dimensions. These are universal, state-independent lower bounds on semi-local integrals of $\langle T_{vv} \rangle$, the energy-momentum flux in a null direction, and the first of this kind for interacting theories in higher dimensions. Our ingredients include the quantum null energy condition (QNEC), strong subadditivity of von Neumann entropies, defect operator expansions, and the vacuum modular Hamiltonians of null intervals and strips. These results are fundamental constraints on null energy in quantum field theories.