Higher Spin Entanglement Entropy

Abstract

In this paper, we develop a perturbation formulation to calculate the single interval higher spin R$\acute{e}$nyi and entanglement entropy for two dimensional conformal field theory with ${\mathcal{W}}_{\infty }(\lambda )$ symmetry. The system is at finite temperature and is deformed by higher spin chemical potential. We manage to compute higher spin R$\acute{e}$nyi entropy with various spin deformations up to order $\mathcal{O}({\mu }^2)$. For spin 3 deformation, we calculate exact higher spin R$\acute{e}$nyi entropy up to $\mathcal{O}({\mu }^4)$. 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 ${\mathcal{R}}_n$ to complex plane and correlation functions of primary fields on complex plane. The method can be applied to general conformal field theories with $\mathcal{W}$ symmetry.

49 pages,1 figure, to be published in JHEP

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