Quantum Correction of the Wilson Line and Entanglement Entropy in the Pure AdS$_3$ Einstein Gravity Theory

TL;DR

This paper computes quantum corrections to Wilson lines and entanglement entropy in pure AdS$_3$ Einstein gravity, revealing a shift in the central charge and demonstrating their equivalence in describing boundary entanglement.

Contribution

It provides the first one-loop calculation linking Wilson lines and entanglement entropy in pure AdS$_3$ gravity, illustrating their equivalence.

Findings

One-loop entanglement entropy shows a central charge shift to 26.

Wilson line and entanglement entropy are equivalent descriptions.

Supports the minimal surface=entanglement entropy conjecture.

Abstract

We calculate the expectation value of the Wilson line in the pure AdS$_3$ Einstein gravity theory and also the entanglement entropy in the boundary theory. Our one-loop calculation of entanglement entropy shows a shift of the central charge 26. Finally, we show that the Wilson line provides the equivalent description to the boundary entanglement entropy. This equivalence leads to a concrete example of the building of "minimum surface=entanglement entropy".