When a local QFT is coupled to gravity, properties of its energy (or more generally the stress tensor) density expectation values play a crucial role in the gravitational dynamics. Classical conjectures of the stress tensor density (known as the energy conditions) are easily violated in QFTs. Conjectures about the quantum versions of the energy conditions (e.g. ANEC, QNEC) were proposed. Much progresses have been made in the recent decade for understanding and proving these quantum energy conditions. Their origins were found surprisingly in the universal properties of the entanglement structures of the QFTs. In this lecture series, I will review the developments related to the quantum energy conditions, emphasizing on the recent progresses of entanglement-based proofs.  

Inviter: Jie-Qiang Wu