  We consider free fermion and free boson CFTs in two dimensions, deformed by a
chemical potential $\mu$ for the spin-three current. For the CFT on the
infinite spatial line, we calculate the finite temperature entanglement entropy
of a single interval perturbatively to second order in $\mu$ in each of the
theories. We find that the result in each case is given by the same non-trivial
function of temperature and interval length. Remarkably, we further obtain the
same formula using a recent Wilson line proposal for the holographic
entanglement entropy, in holomorphically factorized form, associated to the
spin-three black hole in SL(3, R) x SL(3, R) Chern-Simons theory. Our result
suggests that the order $\mu^2$ correction to the entanglement entropy may be
universal for W-algebra CFTs with spin-three chemical potential, and
constitutes a check of the holographic entanglement entropy proposal for higher
spin theories of gravity in AdS_3.
