Higher spin entanglement entropy

In this paper, we develop a perturbation formulation to calculate the single interval higher spin Renyi and entanglement entropy for two dimensional conformal field theory with W-infinity(lambda) symmetry. The system is at finite temperature and is deformed by higher spin chemical potential. We manage to compute higher spin Renyi entropy with various spin deformations up to order O(mu(2)). For spin 3 deformation, we calculate exact higher spin Renyi and entanglement entropy up to O(mu(4))). When lambda = 3, in the large c limit, we find perfect match with tree level holographic higher spin entanglement entropy up to order mu(4) obtained by the Wilson line prescription. We also find quantum corrections to higher spin entanglement entropy which is beyond tree level holographic results. The quantum correction is universal at order mu(4) in the sense that it is independent of lambda. Our computation relies on a multi-valued conformal map from n-sheeted Riemann surface R-n to complex plane and correlation functions of primary fields on complex plane. The method can be applied to general conformal field theories with W symmetry.