Universal correction to higher spin entanglement entropy

We consider conformal field theories in two spacetime dimensions with W-algebra symmetries, deformed by a chemical potential μ for the spin-three current. We show that the order μ2 correction to the R ́enyi and entanglement entropies of a single interval in the deformed theory, on the infinite spatial line and at finite temperature, is universal. The correction is completely determined by the operator product expansion of two spin-three currents, and by the expectation values of the stress tensor, its descendants and its composites, evaluated on the n-sheeted Riemann surface branched along the interval. This explains the recently found agreement of the order μ2 correction across distinct free field CFTs and higher spin black hole solutions holographically dual to CFTs with W-symmetry