Higher spin entanglement entropy at finite temperature with chemical potential

TL;DR

This paper investigates how higher spin fields influence entanglement entropy at finite temperature with chemical potential, using both conformal field theory and holographic Wilson line calculations, revealing exact agreement.

Contribution

It develops a monodromy analysis for two-point functions in ${ m W}_3$-deformed CFTs and matches holographic Wilson line results in spin-3 black hole backgrounds.

Findings

Exact agreement between CFT and holographic calculations.

Extension of monodromy analysis to ${ m W}_3$ deformations.

Insights into higher spin effects on entanglement entropy.

Abstract

It is generally believed that the semiclassical AdS$_3$ higher spin gravity could be described by a two dimensional conformal field theory with ${\cal{W}}$-algebra symmetry in the large central charge limit. In this paper, we study the single interval entanglement entropy on the torus in the CFT with a ${\cW}_3$ deformation. More generally we develop the monodromy analysis to compute the two-point function of the light operators under a thermal density matrix with a ${\cW}_3$ chemical potential to the leading order. Holographically we compute the probe action of the Wilson line in the background of the spin-3 black hole with a chemical potential. We find exact agreement.