OPE of the stress tensors and surface operators

Abstract: We demonstrate that the divergent terms in the OPE of a stress tensor and a line (co-dimension two) operator of general shape in three dimensional spacetime cannot be constructed only from local geometric data depending only on the shape of the line. We verify this holographically for Wilson line operators or equivalently the twist operator corresponding to computing the entanglement entropy using the Ryu-Takayanagi formula. We discuss possible implications of this result.