By rearranging its terms, the Quantum Focusing Conjecture, 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) that can be proven with field theory techniques. We sketch the proof, in the case of a class of conformal filed theories, where the modular Hamiltonian is known, and can be mapped onto the past light-cone. We find that the INEC holds given a condition on an integral of the energy momentum tensor on a finite segment. Finally, we suggest the implications of considering the energy conditions as fundamental and show how it will imply possible derivations of the different focusing conjectures.
Ido Ben-Dayan (Ariel/Palästina): The improved Quantum Null Energy Condition
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