General Results for Higher Spin Wilson Lines and Entanglement in Vasiliev Theory

TL;DR

This paper develops new tools for calculating Wilson lines in 3D higher spin gravity, enabling the computation of entanglement entropy and other quantities in Vasiliev theory, with results consistent with conformal field theory predictions.

Contribution

The paper introduces a method to evaluate SL(N) Wilson lines for arbitrary N and analytically continue to hs[] theory, advancing the computational techniques in higher spin holography.

Findings

Computed entanglement entropy in higher spin black holes.

Established the connection between Wilson lines and W_N vacuum blocks.

Validated results against conformal field theory calculations.

Abstract

We develop tools for the efficient evaluation of Wilson lines in 3D higher spin gravity, and use these to compute entanglement entropy in the hs$[\lambda]$ Vasiliev theory that governs the bulk side of the duality proposal of Gaberdiel and Gopakumar. Our main technical advance is the determination of SL(N) Wilson lines for arbitrary $N$, which, in suitable cases, enables us to analytically continue to hs$[\lambda]$ via $N \rightarrow -\lambda$. We apply this result to compute various quantities of interest, including entanglement entropy expanded perturbatively in the background higher spin charge, chemical potential, and interval size. This includes a computation of entanglement entropy in the higher spin black hole of the Vasiliev theory. These results are consistent with conformal field theory calculations. We also provide an alternative derivation of the Wilson line, by showing how it arises naturally from earlier work on scalar correlators in higher spin theory. The general picture that emerges is consistent with the statement that the SL(N) Wilson line computes the semiclassical $W_N$ vacuum block, and our results provide an explicit result for this object.