旋转AdS3+1超导体的解析特性研究

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"旋转全息超导体的解析研究" 这篇论文主要探讨了在旋转AdS_{3+1}(Anti-de Sitter时空的三维加一旋转版本)背景下的s波全息超导体。研究采用了探针极限(probe limit)的方法，这意味着超导体的行为被视为背景引力场中的一个微扰。文章中，作者Ankur Srivastava和Sunandan Gangopadhyay来自印度S.N. Bose National Centre for Basic Sciences。关键知识点： 1. **旋转AdS_{3+1}时空**: 这是一种具有洛伦兹对称性的时空模型，常用于研究高维引力理论与低维量子场论之间的全息对应关系，即AdS/CFT对应。这里的“旋转”指的是黑洞或时空背景具有角动量，影响了其中的物理过程。 2. **s波全息超导体**: 全息超导体是全息对应中的一个重要概念，它在AdS/CFT对应中模拟了四维时空中的超导现象。s波超导体指的是配对的电子具有零自旋，对应于低能量激发的简并态。 3. **探针极限**: 在这个极限下，超导体的荷载不改变背景时空的几何，使得可以简化问题，只考虑超导体对背景的响应，而忽略其对背景的影响。 4. **匹配方法**: 一种解决边界条件问题的技术，用于连接不同区域的解，例如近黑洞视界和远距离区域的解，以得到整个系统的完整解决方案。 5. **Stürm-Liouville特征值方法**: 这是一种处理线性微分方程系统的方法，特别适用于寻找定态问题的本征值和本征函数。在超导体的研究中，可能用于求解能隙方程和临界温度。 6. **临界温度**: 超导体转变为超导状态的温度，低于这个温度，超导现象出现。通过匹配技术和Stürm-Liouville方法计算得到的临界温度是一致的。 7. **condensation算符**: 在超导体中，当温度下降到临界温度以下时，某些粒子会形成配对，导致凝聚，这可以通过分析方法来确定。 8. **旋转参数影响**: 黑洞的旋转参数（角动量）对临界温度有直接影响，意味着旋转会影响超导体的相变行为。 9. **数值与解析结果比较**: 作者通过两种不同的分析方法得到了一致的结果，这增强了对理论模型的信任，并验证了之前通过数值模拟得出的结论。这篇论文深入研究了旋转AdS_{3+1}时空中的s波全息超导体，通过匹配方法和Stürm-Liouville特征值方法，得出了临界温度的解析表达，并讨论了旋转参数对超导性的影响。这些研究成果对于理解全息超导现象和黑洞物理学有重要意义。

Eur. Phys. J. C (2019) 79:340

https://doi.org/10.1140/epjc/s10052-019-6834-0

Regular Article - Theoretical Physics

Analytic investigation of rotating holographic superconductors

Ankur Srivastav

, Sunandan Gangopadhyay

Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake City, Kolkata 700106, India

Received: 23 February 2019 / Accepted: 29 March 2019 / Published online: 15 April 2019

Abstract In this paper we have investigated, in the probe

limit, s-wave holographic superconductors in rotating

AdS

3+1

spacetime using the matching method as well as

the Stürm–Liouville eigenvalue approach. We have calcu-

lated the critical temperature using the matching technique

in such a setting and our results are in agreement with pre-

viously reported results obtained using the Stürm–Liouville

approach. We have then obtained the condensation operators

using both analytical methods. The results obtained by both

these techniques share the same features as found numeri-

cally. We observe that the rotation parameter of the black

hole affects the critical temperature and the condensation

operator in a non-trivial way.

1 Introduction

High-T

superconductors were discovered by Bednorz and

Müller [1]. These are prototype of the so called strongly cor-

related systems in condensed matter physics. Such systems

generically fall under strongly coupled ﬁeld theories. How-

ever, due to strong coupling these systems are hard to tame

using traditional ﬁeld theoretic approaches. In the last decade,

the AdS/CFT correspondence has emerged as a powerful tool

to study such systems. The AdS/CFT correspondence origi-

nated from string theory and was discovered by Maldacena

in 1997 [2]. The conjecture implies that a gravity theory in

a(d + 1)-dimensional anti-de Sitter (AdS) spacetime is an

exact dual to a conformal ﬁeld theory (CFT) living on the

d-dimensional boundary of the bulk spacetime.

The importance of the gauge/gravity correspondence in

strongly coupled systems was realized in 2008 when Gubser

showed that for an asymptotic AdS black hole, near to its hori-

zon, U(1) gauge symmetry spontaneously breaks giving rise

e-mail: ankursrivastav@bose.res.in

e-mails: sunandan.gangopadhyay@gmail.com;

sunandan.gangopadhyay@bose.res.in

to the phenomenon of superconductivity in the vicinity of the

black hole horizon [3]. Immediately using this result Hart-

noll, Herzog, and Horowitz used the AdS/CFT correspon-

dence to study holographic superconductors which mim-

ics the properties of high-T

superconductors [4,5]. Since

then various aspects of such holographic superconductors

have been explored in various black hole space-time set-

tings [6–11]. Most of the holographic superconductors con-

sidered so far are constructed using non-rotating black hole

spacetime. However, even before the discovery of AdS/CFT

correspondence, rotating black holes were known to show

Meissner like effect [12,13]. This motivates us to investi-

gate about the role of rotating black holes in holographic

superconductor models. Such a study was ﬁrst initiated in

[14] where the study of spontaneous symmetry breaking in

3 +1-dimensional rotating, charged AdS black hole was car-

ried out. It was observed that the superconducting order gets

destroyed for a particular value of the rotation just below

the critical temperature. Recently, a holographic supercon-

ductor model in rotating black hole spacetime was studied

in [15]. Here, the Stürm–Liouville (SL) eigenvalue approach

was used to obtain the critical temperature analytically. How-

ever, the condensation operator was studied numerically. Our

aim in this paper is to provide an analytical approach to rotat-

ing holographic superconductors and obtain the critical tem-

perature as well as the condensation operator. We shall ﬁrst

use the matching technique to obtain the critical temperature

for both possible values of the conformal dimension. This

technique was introduced in [16] and involves the match-

ing of the solutions to the matter and gauge ﬁeld equations

near the black hole horizon and the AdS boundary. We then

compare our results with those obtained from the SL tech-

nique in [15]. Using the matching approach, we then obtain

the values of the condensation operator. Further, we also

apply the SL eigenvalue approach to obtain the condensa-

tion values and compare the results with those obtained by

us using the matching technique and also with the numeri-

cal results in the literature. All the calculations in this paper

123

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