The quantum focusing conjecture and the improved energy condition - Ido Ben-Dayan (Journal of High Energy Physics, 2024)
Abstract 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 ≥ ħ 2 π A S out ′ ′ − 1 2 θ S out ′ $$ T_{kk}\ge \frac{\mathrm{\hbar}}{2π \mathcal{A}}\left(S_{out}^{′ ′ }-\frac{1}{2}θ S_{out}^{′}\right) $$ , 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.