  A holographic correspondence has been recently developed between higher spin
theories in three-dimensional anti-de Sitter space (AdS_3) and two-dimensional
Conformal Field Theories (CFTs) with extended symmetries. A class of such
dualities involves SL(N,R)\times SL(N,R) Chern-Simons gauge theories in the
(2+1)-dimensional bulk spacetime, and CFTs with W_N symmetry algebras on the
(1+1)-dimensional boundary. The topological character of the Chern-Simons
theory forces one to reconsider standard geometric notions such as black hole
horizons and entropy, as well as the usual holographic dictionary. Motivated by
this challenge, in this note we present a proposal to compute entanglement
entropy in the W_N CFTs via holographic methods. In particular, we introduce a
functional constructed from Wilson lines in the bulk Chern-Simons theory that
captures the entanglement entropy in the CFTs dual to standard AdS_3 gravity,
corresponding to SL(2,R)\times SL(2,R) gauge group, and admits an immediate
generalization to the higher spin case. We explicitly evaluate this functional
for several known solutions of the Chern-Simons theory, including charged black
holes dual to thermal CFT states carrying higher spin charge, and show that it
reproduces expected features of entanglement entropy, study whether it obeys
strong subadditivity, and moreover show that it reduces to the thermal entropy
in the appropriate limit.
