Abstract
The (F1,D2,D8) brane configuration with $Lif_4^{(2)}\times {S}^1\times S^5$ 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 $Lif_4^{(3)}\times S^1\times S^5$ vacua in IR. We study the entanglement entropy on the boundary of this spacetime for the strip and the disc 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 the light of first law of entanglement thermodynamics.
Highlights
In this report we aim to study holographic entanglement entropy (HEE) [25] of the excited Lifshitz subsystems which are either a disk or a strip in a perturbative framework
II we review salient features of Lifð42Þ × S1 × S5 vacua with IR excitations in massive type IIA (mIIA) theory
For asymptotically AdS spacetime dual to a CFT, the entanglement entropy can be calculated by the RyuTakayanagi formula [25]
Summary
The gauge-gravity correspondence [1,2,3] has got a nonrelativistic version where strongly coupled quantum theories at critical points can be studied [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. In this work we shall mainly study entanglement entropy of the excitations in asymptotically Lifð4a1⁄42Þ × S1 × S5 background The latter is a Lifshitz vacua in massive type IIA (mIIA) theory [20,21] with the dynamical exponent of time being a 1⁄4 2. We shall study a class of stringlike excitations which themselves form solutions of massive IIA supergravity and explicitly involve the B field [21] These induce running of dilaton as well. The theory gives rise to well-known FreundRubin-type vacua AdS4 × S6 [24], the supersymmetric domain- walls or D8-branes [29,30,31,32,33], ðD6; D8Þ, ðD4; D6; D8Þ bound states [34,35] and Galilean-AdS geometries [12,13] In all of these massive tensor field plays a key role. Note the zI-dependent excitations at zero temperature are mainly in the form of charge excitations, along with nontrivial entanglement chemical potential, as we would see
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