  We provide the first example of local quantum energy conditions in quantum
field theories that are not Lorentz invariant. We focus on field theories in
two dimensions with infinite-dimensional symmetries, like the ones governed by
the Bondi-van der Burg-Metzner-Sachs group that appear in the context of flat
space holography. Reminiscent of holographic results on the quantum null energy
condition, we prove that our new energy conditions saturate for states in the
field theory that are dual to vacuum solutions of three-dimensional Einstein
gravity with vanishing cosmological constant.
