Local quantum energy conditions in non-Lorentz-invariant quantum field theories

TL;DR

This work addresses local quantum energy conditions in non-Lorentz-invariant QFTs by constructing the first explicit 𝔟ms_3-invariant QECs using flat-space holography. It develops a uniformization-based framework and leverages the flat-space limit of QNEC to derive saturated relations between holographic entanglement entropy and 𝔟ms_3 energy charges, yielding precise EE transformations and two saturation equations. The main results include explicit EE formulas for 𝔟ms_3-invariant theories, transformation laws under BMS symmetries, and the flat-space QECs: $2\pi\langle\mathcal{T}_L\rangle \ge S_L''+6c_L S_L'^2$ for $c_M=0$ and $2\pi\langle\mathcal{T}_M\rangle \ge \dot{S}_M'+6c_M\dot{S}_M^2$ for $c_M\neq0$, with saturations on flat-space vacua. These results establish QECs as natural analogs of QNEC in 𝔟ms_3-invariant QFTs and open avenues for intrinsic field-theoretic derivations and extensions to warped CFTs and tensionless string theories.

Abstract

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.