The $(F1,D2,D8)$ brane configuration with $Li{f}_4^{(2)}\times S^1\times S^5$ geometry is a known Lifshitz vacua supported by massive $B_{\mu \nu }$ field in type IIA theory. This system allows exact IR excitations which couple to massless modes of the fundamental string. Due to these massless modes the solutions have a flow to a dilatonic $Li{f}_4^{(3)}\times S^1\times S^5$ vacua in IR. We study the entanglement entropy on the boundary of this spacetime for the strip and the disk subsystems. To our surprise net entropy density of the excitations at first order is found to be independent of the typical size of subsystems. We interpret our results in light of the first law of entanglement thermodynamics.

中文翻译：

---

带弦激励的Lif4（2）×S1×S5时空的全息纠缠熵

这 $（F\mathrm{1个}，d\mathrm{2个}，d8）$ 麸皮配置 $\mathrm{大号}\mathrm{一世}{F}_4^{（\mathrm{2个}）}\times {\mathrm{小号}}^{\mathrm{1个}}\times {\mathrm{小号}}^5$ 几何形状是由大规模支持的已知的Lifshitz真空 ${乙}_{\mu \nu }$IIA型理论领域。该系统允许精确的IR激发，该激发与基本弦的无质量模式耦合。由于这些无质量模式，解决方案可以流向膨胀$\mathrm{大号}\mathrm{一世}{F}_4^{（3）}\times {\mathrm{小号}}^{\mathrm{1个}}\times {\mathrm{小号}}^5$IR中的真空。我们研究了带状和磁盘子系统在此时空边界上的纠缠熵。令我们惊讶的是，发现一阶激发的净熵密度与子系统的典型大小无关。我们根据纠缠热力学的第一定律解释我们的结果。