黑色非超对称D3麸皮的全息纠缠熵与热力学分析

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本文主要探讨的是"黑色"非超对称(D3)膜在IIB型弦理论中的全息纠缠熵和纠缠热力学。D3膜在超对称（susy）和非超对称情况下都具有一种特殊的性质，即存在解耦极限，这使得它们能够与AdS/CFT对偶性相联系。在非超对称D3膜的情况下，对应的量子场论（QFT）不具备保形性和超对称性，其喉部几何提供了理论模型的独特描述。作者首先运用全息技术，从解耦的"黑色"非多余D3膜的几何结构出发，计算了在这种有限温度条件下QFT的小子系统的纠缠熵。纠缠熵是量子信息理论中的一个重要概念，它反映了量子系统内部的量子纠缠程度，对于理解和刻画量子系统的复杂性至关重要。接着，研究者深入探讨了这种QFT在弱激发态下的纠缠热力学，特别是关注了子系统大小与其相关的纠缠温度以及垂直于纠缠表面的纠缠压力之间的关系。他们发现，对于较小的子系统，该背景符合纠缠热力学的第一定律，即纠缠熵与子系统的大小成反比，同时纠缠温度和纠缠压力之间存在着一定的比例关系，这是量子系统中一个基本的热力学规律。此外，文章还揭示了一个有趣的交叉现象：纠缠熵在高温环境下与热熵产生了交叉，这表明在不同的能量尺度下，纠缠和热力学行为可能存在意想不到的关联。这一发现对于理解量子系统在不同物理条件下的行为具有重要意义，尤其是在黑洞和量子信息等领域。本文通过对"黑色"非超对称D3膜的全息分析，不仅深化了我们对非超对称AdS/CFT对应的理解，还扩展了我们对量子纠缠和热力学在非标准量子场论中的应用知识。这些研究成果为探索量子引力、量子信息和黑洞物理等领域提供了新的视角和工具。

Physics Letters B 781 (2018) 232–237

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Holographic entanglement entropy and entanglement thermodynamics

of ‘black’ non-susy D3 brane

Aranya Bhattacharya

a,b

, Shibaji Roy

a,b,∗

Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700064, India

Homi Bhabha National Institute, Training School Complex, Anushakti Nagar , Mumbai 400085, India

a r t i c l e i n f o a b s t r a c t

Article history:

Received

14 December 2017

Received

in revised form 4 April 2018

Accepted

6 April 2018

Available

online 9 April 2018

Editor: M.

Cveti

Like BPS D3 brane, the non-supersymmetric (non-susy) D3 brane of type IIB string theory is also known

to have a decoupling limit and leads to a non-supersymmetric AdS/CFT correspondence. The throat

geometry in this case represents a QFT which is neither conformal nor supersymmetric. The ‘black’

version of the non-susy D3 brane in the decoupling limit describes a QFT at ﬁnite temperature. Here we

ﬁrst compute the entanglement entropy for small subsystem of such QFT from the decoupled geometry of

‘black’ non-susy D3 brane using holographic technique. Then we study the entanglement thermodynamics

for the weakly excited states of this QFT from the asymptotically AdS geometry of the decoupled ‘black’

non-susy D3 brane. We observe that for small subsystem this background indeed satisﬁes a ﬁrst law like

relation with a universal (entanglement) temperature inversely proportional to the size of the subsystem

and an (entanglement) pressure normal to the entangling surface. Finally we show how the entanglement

entropy makes a cross-over to the thermal entropy at high temperature.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

The entanglement entropy (EE) is a measure of quantum infor-

mation

encoded in a quantum system. In particular, for a bipartite

system the EE of a subsystem A is the von Neumann entropy and

is deﬁned as S

=−Tr(ρ

log ρ

), where ρ

= Tr

(ρ

tot

) is the re-

duced

density matrix on A obtained by tracing out on B, the com-

plement

of A, of the density matrix of the total system ρ

tot

(see,

for example, [1–7] including some reviews). It is useful for many

body systems to describe various quantum phases of matter and

serves as an order parameter for the quantum phase transitions

which occur near zero temperature [8–12]. The density matrix can

be carefully deﬁned in the continuum and therefore, EE can be cal-

culated

in a QFT in principle using the so-called replica trick (see,

for example [13]). However, the actual computation can be done

quite generally only in low dimensional CFT

d+1

(d < 2) [3,4]. For

higher dimensions the computation of EE becomes intractable ex-

cept

for some special cases, like free ﬁeld QFT in three dimensions

and also for CFT

[13].

Ryu

and Takayanagi [14,15], motivated by the Bekenstein–

Hawking

entropy formula, gave a prescription to compute EE in

Corresponding author.

E-mail

addresses: aranya .bhattacharya @saha .ac .in (A. Bhattacharya),

shibaji .roy @saha .ac .in (S. Roy).

any dimensions using the idea of AdS/CFT [16,17]. According to

them, the holographic EE (HEE) of the subsystem A in the gravity

dual is given by [14]

Area(γ

min

)

(1)

where γ

min

is the d-dimensional minimal area (time-sliced)

surface in AdS

d+2

space whose boundary matches with the

boundary of the subsystem A, i.e., ∂γ

min

= ∂ A and G

is the

(d + 2)-dimensional Newton’s constant. The HEE given in (1) has

been checked [14]to agree with the QFT results in lower di-

mensions.

In higher dimensions also they give correct qualitative

behaviors. In thermodynamics the entropy of a system can be

increased by injecting energy to the system, where the proportion-

ality

constant is given by the inverse of temperature. This leads

to an energy conservation relation E = T S, the ﬁrst law of

thermodynamics. An analogous problem was addressed in [18]for

the EE, i.e., to see how the EE of a certain region grows with the

increase in energy. Here the EE is computed using AdS/CFT. The

excited state of a CFT is given by the deformation of AdS whose EE

can be computed using (1). This is then compared with the time

component of the boundary stress tensor T

or the energy density.

For a small subsystem A, the total energy is found to be propor-

tional

to the increase in EE and the proportionality constant is c/,

https://doi.org/10.1016/j.physletb.2018.04.011

0370-2693/

SCOAP

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