The quantum focusing conjecture and the improved energy condition

By rearranging its terms, the Quantum Focusing Conjecture (QFC) can be viewed as a quantum energy condition, and we can consider various limits. A recent restricted version is a limiting form where the quantum focusing vanishes Θ → 0, and has been proven for Braneworld scenario. As a result, we derive an improved quantum null energy condition (INEC) T_kk≥ħ2πAS_out^′′−12θS_out^′, that can be proven with field theory techniques. We sketch the beginning of a proof, and briefly discuss possible interpretations in the absence of one.