OPE of the stress tensors and surface operators

TL;DR

This paper shows that divergences in the operator product expansion of stress tensors and surface operators cannot be solely determined by local geometric data, with holographic verification for Wilson lines and entanglement entropy.

Contribution

It reveals a fundamental limitation in constructing divergences from local geometric data in OPEs involving surface operators, supported by holographic analysis.

Findings

Divergent terms in OPEs are not solely geometric.

Holographic verification for Wilson lines at d=3.

Implications for understanding surface operator divergences.

Abstract

We demonstrate that the divergent terms in the OPE of a stress tensor and a surface operator of general shape cannot be constructed only from local geometric data depending only on the shape of the surface. We verify this holographically at d=3 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.