Peculiarity of the Entanglement for $Lif_4^{(2)}\times {S}^1\times S^5$ Spacetime with String Excitations

Sabyasachi Maulik, Harvendra Singh

Published Nov 25, 2019• 0 citations

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.

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Peculiarity of the Entanglement for $Lif_4^{(2)}\times {S}^1\times S^5$ Spacetime with String ExcitationsPeculiarity of the Entanglement for $Lif_4^{(2)}\times {S}^1\times S^5$ Spacetime with String Excitations

Sabyasachi Maulik, Harvendra Singh

Published Nov 25, 2019• 0 citations

OpenAlex

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.

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arXiv:1905.06708May 16, 20191 citation

Peculiarity of the Entanglement for

Lif_4^{(2)}\times {S}^1\times S^5

Spacetime with String Excitations

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

We study certain classes of

{g}_{++}

deformations of theories arising in gauge/string realizations of nonrelativistic holography, some of which pertain to

z=2

Lifshitz theories while others (pertaining to hyperscaling violation) comprise certain classes of excited states. Building on previous work, we consider holographic entanglement entropy for spacelike strip subsystems in a highly boosted (lightlike) limit, where the strip is stretched along the null

{x}^{+}

plane. The leading divergence in entanglement in this null limit for these excited states is milder than the usual area law for spacelike subsystems in ground states. For ground states, the entanglement vanishes, perhaps consistent with ultralocality. We discuss this briefly from a field theory perspective. We also present some simple free lightfront field theory examples in excited states where correlators are nonvanishing.

w

. Both the zero-temperature backgrounds and the finite-temperature counterparts are exact solutions of Einstein-Maxwell-dilaton theory. For the extremal case we consider the examples where the entangling regions are a strip and a sphere. We find that the leading-order behavior of the entanglement entropy always exhibits a volume law when the size of the entangling region is sufficiently small. We also clarify the condition under which the next-to-leading-order result is universal. For the finite-temperature case we obtain analytic expressions in both the high-temperature and low-temperature limits. In the former case the leading-order result approaches the thermal entropy, while the finite contribution to the entanglement entropy at extremality can be extracted by taking the zero-temperature limit in the latter case. Moreover, we observe some peculiar properties of the holographic entanglement entropy when

w=1

D

-dimensional bosonic string theory, the entanglement entropy of spin

1

subsystem and the system of all the spin values is given by

D{\log{λ_0}}+{D\over{λ_0}}\sum_{N=3}^\infty{{|β(N)|}\over{λ(N)}} {\log{({{λ(N)}\over{|β(N)|}})}}

, where

λ(N)

is the weighted number of partitions of

N

β(N)={{(N-1)ζ(3)-ζ(2)}\over{(N-1)^4}}

and

λ_0=\sum_{N=1}^{\infty}{{β(N)}\over{λ(N)}}

(

ζ

is Riemann's zeta-function). The first term,

D{\log{λ_0}}

, represents the entanglement swapping between string vacuum and string excitations. We generalize this result to obtain the entanglement for a subsystem of a given spin

s

in a given space-time dimension. We also discuss how open string field theory may be used to study the entanglement of systems other than higher spin excitations in string theory.