Entropy Variations and Light Ray Operators from Replica Defects

Understand

We study the defect operator product expansion (OPE) of displacement operators in free and interacting conformal field theories using replica methods.

• We show that as $n$ approaches $1$ a contact term can emerge when the OPE contains defect operators of twist $d-2$.
• For interacting theories and general states we give evidence that the only possibility is from the defect operator that becomes the stress tensor in the $n\to 1$ limit.
• This implies that the quantum null energy condition (QNEC) is always saturated for CFTs with a twist gap.