Quantum Focusing Conjecture (QFC)

Establish that in semiclassical gravity the quantum expansion functional Theta cannot increase along any null hypersurface, i.e., for any foliation V_lambda of a null hypersurface and any generator position y, show that partial_Theta[V_lambda,y]/partial_lambda <= 0 holds everywhere.

Background

The QFC is a proposed quantum generalization of the classical focusing theorem and, if true, implies a wide array of consequences including the Bekenstein bound, generalized second law, and the Quantum Null Energy Condition. It also underpins entanglement wedge nesting and boundary causality in holography. The thesis reviews the QFC and explores its implications and tests, including in JT gravity.