On the next-to-leading holographic entanglement entropy in $AdS_{3}/CFT_{2}$

TL;DR

This paper computes subleading one-loop corrections to holographic entanglement entropy in $AdS_{3}/CFT_{2}$ for two disjoint intervals, focusing on bulk higher-spin currents of spin $s$ and bulk scalars of dimension $ riangle$. Using Schottky uniformization and the replica trick, the authors derive closed-form CDW contributions for the higher-spin case and detailed scalar-series expansions, validating the gravity results against explicit CFT calculations up to $ ext{O}(x^{2 riangle+5})$ and $ ext{O}(x^{4s+2})$ for spins $s=2,3,4$. A key technical advance is the $n o1$ simplification in the entanglement limit, which isolates the relevant descendants (mainly $oldsymbol{∂}$-driven) and yields compact expressions, including a universal hypergeometric form for CDW terms and a closed formula for the leading $2$-CDW coefficient $oldsymbol{ ext{σ}}_s$. The results deepen the AdS/CFT tests by explicitly coupling bulk higher-spin dynamics and scalar fields to entanglement entropy in the two-interval setting, offering practical closed-form tools and illuminating the operator content governing subleading holographic entanglement corrections.

Abstract

We reconsider the one-loop correction to the holographic entanglement entropy in $AdS_{3}/CFT_{2}$ by analysing the contributions due to a bulk higher spin $s$ current or a scalar field with scaling dimension $Δ$. We consider the two-interval case and work perturbatively in their small cross ratio $x$. We provide various results for the entanglement entropy due to the so-called CDW elements of the associated Schottky uniformization group. In particular, in the higher spin current case, we obtain a closed formula for all the contributions of the form $\mathcal O(x^{2s+p})$ up to $\mathcal O(x^{4s})$, where 2-CDW elements are relevant. In the scalar field case, we calculate the similar contributions for generic values of $Δ$. The terms up to $\mathcal O(x^{2Δ+5})$ are compared with an explicit CFT calculation with full agreement. The analysis exploits various simplifications which are valid in the strict entanglement limit of the Rényi entropy. This allows to identify in a clean way the relevant operators that provide the gravity result. The 2-CDW contributions are also analysed and a closed formula for the leading $\mathcal O(x^{4s})$ coefficient is presented as a function of the generic spin $s$. As a specific application, we combine the CDW and 2-CDW calculations and present the complete $\mathcal O(x^{4s+2})$ entanglement entropy for a spin $s=2,3,4$ higher spin current.