Entanglement Entropy Evolution under Double-trace Deformation

TL;DR

This paper investigates how bulk entanglement entropy evolves in a BTZ black hole background under double-trace deformation, revealing it decreases for large black holes and increases for small black holes, consistent with holographic principles.

Contribution

It provides the first detailed analysis of bulk entanglement entropy evolution under double-trace deformation in a BTZ black hole background using heat kernel methods.

Findings

Bulk entanglement entropy decreases in large black hole limit.

Bulk entanglement entropy increases in small black hole limit.

Results align with the holographic c-theorem.

Abstract

In this paper, we study the bulk entanglement entropy evolution in conical BTZ black bole background using the heat kernel method. This is motivated by exploring the new examples where quantum corrections of entanglement entropy give the leading contribution. We find that in the large black hole limit the bulk entanglement entropy decreases under the double-trace deformation which is consistent with the holographic $c$ theorem and in the small black hole limit the bulk entanglement entropy increases under the double-trace deformation.