Jerome P. Gauntlett, Julian Sonner, Toby Wiseman
Using seven-dimensional Sasaki-Einstein spaces we construct solutions of D=11 supergravity that are holographically dual to superconductors in three spacetime dimensions. Our numerical results indicate a new zero temperature solution dual to a quantum critical point.
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Holographic spectral functions for Sasaki-Einstein 5-manifolds
研究一般Sasaki-Einstein 5维流形的全息谱函数，包括超对称指数量子、超对称ζ函数和超对称决定式，通过分析ζ函数的解析结构计算曲率平方积分和次领界全息反常。
We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of D=11 supergravity compactified on squashed seven-dimensional Sasaki-Einstein manifolds. Such reductions are of interest, for example, in that they have $(2+1)$-dimensional holographic duals, and the fermionic content and their interactions with charged scalars are an important aspect of their applications. We derive the lower-dimensional equations of motion for the fermions and exhibit their couplings to the various bosonic modes present in the truncations under consideration, which m…
Towards Supergravity Duals of Chiral Symmetry Breaking in Sasaki-Einstein Cascading Quiver Theories
我们构造了Sasaki-Einstein空间Y^{p，q}上锥的复结构的一阶变形，并明确地检验了超对称性.这个空间是一个中心元素的全息对偶的手征对称性破缺的一大类级联的量子力学理论。我们讨论的解决方案描述了一个堆栈的N D3膜和M分数D3膜的变形空间的尖端。
We present prescriptions for obtaining the central charges, $a$ and $c$, of a four dimensional superconformal quantum field theory from the superconformal index. At infinite $N$, for holographic theories dual to Sasaki-Einstein 5-manifolds the prescriptions give the $\mathcal{O}(1)$ parts of the central charges. This allows us, among other things, to show the exact AdS/CFT matching of $a$ and $c$ for arbitrary toric quiver CFTs without adjoint matter that are dual to smooth Sasaki-Einstein 5-manifolds. In addition, we include evidence from non-holographic theories for the applicability of thes…
I review recent work on holographic superconductivity with Einstein-Gauss-Bonnet gravity, and show how the critical temperature of the superconductor depends on both gravitational backreaction and the Gauss-Bonnet parameter, using both analytic and numerical arguments. I also review computations of the conductivity, finding the energy gap, and demonstrating that there is no universal gap ratio, $ω_g/T_c$, for these superconductors.
Recent work on holographic superconductivity and gravitational duals of systems with non-relativistic conformal symmetry have made use of consistent truncations of D=10 and D=11 supergravity retaining some massive modes in the Kaluza-Klein tower. In this paper we focus on reductions of IIB supergravity to five dimensions on a Sasaki-Einstein manifold, and extend these previous truncations to encompass the entire bosonic sector of gauged D=5, N=2 supergravity coupled to massive multiplets up to the second Kaluza-Klein level. We conjecture that a necessary condition for the consistency of massiv…
We investigate the effects of Lifshitz dynamical critical exponent z on a family of minimal D=4+1 holographic superconducting models, with a particular focus on magnetic phenomena. We see that it is possible to have a consistent Ginzburg-Landau approach to holographic superconductivity in a Lifshitz background. By following this phenomenological approach we are able to compute a wide array of physical quantities. We also calculate the Ginzburg-Landau parameter for different condensates, and conclude that in systems with higher dynamical critical exponent, vortex formation is more strongly unfa…
A note on the Holographic model for color superconductivity in d-dimension without confinement phase
本文探讨了在d维反德西特空间中，无束缚相的颜色超导模型的共形场论及其方程状态研究。
We construct general models for holographic superconductivity parametrized by three couplings which are functions of a real scalar field and show that under general assumptions they describe superconducting phase transitions. While some features are universal and model independent, important aspects of the quantum critical behavior strongly depend on the choice of couplings, such as the order of the phase transition and critical exponents of second-order phase transitions. In particular, we study a one-parameter model where the phase transition changes from second to first order above some cri…
We construct a family of minimal phenomenological models for holographic superconductors in d=4+1 AdS spacetime and study the effect of scalar and gauge field fluctuations. By making a Ginzburg-Landau interpretation of the dual field theory, we determine through holographic techniques a phenomenological Ginzburg-Landau Lagrangian and the temperature dependence of physical quantities in the superconducting phase. We obtain insight on the behaviour of the Ginzburg-Landau parameter and whether the systems behaves as a Type I or Type II superconductor. Finally, we apply a constant external magneti…
We present the new method to calculate the critical temperature as a function of $Δ$, conformal dimension of the cooper operator. We find that, in the regime $1/2\leq Δ<1$ where the AC conductivity does not show a gap, the critical temperature is not well defined. We also got expression of AC conductivity for $Δ=2$, which agrees with numerical result in the probe approximation.
We study the matrix models that result from localization of the partition functions of N=2 Chern-Simons-matter theories on the three-sphere. A large class of such theories are conjectured to be holographically dual to M-theory on Sasaki-Einstein seven-manifolds. We study the M-theory limit (large N and fixed Chern-Simons levels) of these matrix models for various examples, and show that in this limit the free energy reproduces the expected AdS/CFT result of N^{3/2}/Vol(Y)^{1/2}, where Vol(Y) is the volume of the corresponding Sasaki-Einstein metric. More generally we conjecture a relation betw…
We holographically study supersymmetric deformations of $N=3$ and $N=1$ superconformal field theories (SCFTs) in three dimensions using four-dimensional $N=4$ gauged supergravity coupled to three-vector multiplets with non-semisimple $SO(3)\ltimes (\mathbf{T}^3,\hat{\mathbf{T}}^3)$ gauge group. This gauged supergravity can be obtained from a truncation of eleven-dimensional supergravity on a tri-sasakian manifold and admits both $N=1,3$ supersymmetric and stable non-supersymmetric $AdS_4$ critical points. We analyze the BPS equations for $SO(3)$ singlet scalars in details and study possible su…
Holographic model for color superconductivity in d-dimension bulk without confinement phase
本文将色超导全息模型从传统6维推广到d维AdS空间，研究无禁闭相下SU(N_c)规范理论中的色超导现象，并确定了N_c=2时模型有效的维度范围。
We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of type IIB supergravity compactified on squashed five-dimensional Sasaki-Einstein manifolds. We derive the lower dimensional equations of motion and effective action, and comment on the supersymmetry of the resulting theory, which is consistent with N=4 gauged supergravity in $d=5$, coupled to two vector multiplets. We compute fermion masses by linearizing around two $AdS_{5}$ vacua of the theory: one that breaks N=4 down to N=2 spontaneously, and a second one which preserves no supersy…
Remark on the Emergence of Color Superconductivity for Gauge Theories in General Spacetime Dimensions from simple Holographic Models
本文通过d维AdS空间中的爱因斯坦-麦克斯韦全息模型，研究一般时空维度下颜色超导相及其禁闭-退禁闭相变，并给出N_c=2 CSC相在d=4时的条件。
A holographic bottom-up model used in studying the superconducting system is applied to search for the color superconducting phase of supersymmetric Yang-Mills theory. We apply the probe analysis of this model to the supersymmetric Yang-Mills theory in both the confinement and deconfinement phases. In this analysis, we find the color superconductivity in both phases when the baryon chemical potential exceeds a certain critical value. This result implies that, above the critical chemical potential, a color non-singlet diquark operator, namely the Cooper pair, has its vacuum expectation value ev…
We study holographic superconductivity by expanding the equations in the inverse of the number of spacetime dimensions D. We obtain an analytic expression for the critical temperature as a function of the conformal dimension of the condensate operator. Its accuracy for 3+1-dimensional superconductors is better than 15%. The analysis reveals a simple, and quantitative, explanation for the onset of the superconducting instability, as well as universal features of holographic superconductivity in the large D limit. In particular, this allows to easily compute the effects of backreaction on the cr…
We study holographic dual descriptions of very special conformal field theories with the T(2) symmetry. After constructing solutions in effective five dimensional Einstein gravity coupled with massive two-form fields, we uplift them to the ten dimensional type IIB supergravity, via a consistent truncation ansatz, to derive new analytical solutions in string theory. From the Kaluza-Klein ansatz in terms of the internal Sasaki-Einstein space, we obtain their field theory interpretation with concrete realizations in a large class of holographic $\mathcal{N}=1$ supersymmetric conformal field theor…
We consider the generalization of the S-duality transformation previously investigated in the context of the FQHE and s-wave superconductivity to p-wave superconductivity in 2+1 dimensions in the framework of the AdS/CFT correspondence. The vector Cooper condensate transforms under the S-duality action to the pseudovector condensate at the dual side. The 3+1-dimensional Einstein-Yang-Mills theory, the holographic dual to p-wave superconductivity, is used to investigate the S-duality action via the AdS/CFT correspondence. It is shown that in order to implement the duality transformation, chemic…
We perform a perturbative (near-critical) analysis of the stability of an asymptotically Schroedinger Reissner-Nordstrom black hole with respect to generation of charged scalar hair. We find that apart from the expected instability at low temperatures typical of holographic models of superconductivity, in the presence of certain operators a similar instability appears as well at high temperatures. We propose that the reason for such a phase diagram could be due to peculiar features of the dual gauge theory or the failure of the model to provide a consistent holographic dual of a non-relativist…
We consider CFT's arising from branes probing singularities of internal manifolds. We focus on holographic models with internal space including arbtirary Sasaki-Einstein manifolds coming from CY as well as arbitrary sphere quotients. In all these cases we show that there is a universal upper bound (depending only on the spacetime dimension) for the conformal dimension of the first non-trivial spin 2 operator in the dual CFT and a minimal diameter (in AdS units) for the internal space of the holographic dual and conjecture it holds for all CFT's.
We study compactifications of an infinite family of four-dimensional $\mathcal{N}=1$ SCFTs on a Riemann surface in the presence of arbitrary background fluxes for global symmetries. The four-dimensional parent theories have holographic Sasaki-Einstein duals in type IIB string theory. We compute central charges and R-charges of baryonic operators in the resulting two-dimensional $\mathcal{N}=(0,2)$ theories in three distinct ways: from the field theory side utilizing c-extremization, its recently discovered geometric dual formulation, and holographically using new AdS$_3$ duals of two-dimension…
We study the condensation of a charged scalar field in a $(3+1)$-dimensional asymptotically AdS background in the context of Einsteinian cubic gravity, featuring a holographic superconductor with higher curvature corrections corresponding to a CFT with a non-vanishing value of the stress tensor three-point function $t_4$. As it was previously noticed for higher dimensional Gauss-Bonnet theory, we observe that the critical temperature of the superconducting phase transition is lowered as the higher curvature coupling grows.
In this paper, we consider deformed STU model in four dimensions including both electric and magnetic charges. Using AdS/CFT correspondence, we study holographic superconductor and obtain transport properties like electrical and thermal conductivities. We obtain transport properties in terms of the black hole magnetic charge and interpret it as magnetic monopole of dual field theory. We find that presence of magnetic charge is necessary to have maximum conductivities, and existence of magnetic monopole with a critical charge (137 e) to reach the maximum superconductivity is important. Also, we…
Numerical Sasaki--Einstein metrics and harmonic forms on del Pezzo links
本文数值构造了del Pezzo曲面链环上的Sasaki--Einstein度规及调和形式，通过多项式与神经网络逼近Guillemin势，达到高精度，并验证了方法的有效性，为全息背景研究提供数据。
Four lectures on holography and the AdS/CFT correspondence applied to condensed matter systems. The first lecture introduces the concept of a quantum phase transition. The second lecture discusses linear response theory and Ward identities. The third lecture presents transport coefficients derived from AdS/CFT that should be applicable in the quantum critical region associated to a quantum phase transition. The fourth lecture builds in the physics of a superconducting or superfluid phase transition to the simple holographic model of the third lecture.
In this note, we discuss the basic elements that should appear in a gravitational system dual to a confining gauge theory displaying color superconductivity at large baryon density. We consider a simple system with these minimal elements, and show that for a range of parameters, the phase structure of this model as a function of temperature and baryon chemical potential exhibits phases that can be identified with confined, deconfined, and color superconducting phases in the dual field theory. We find that the critical temperature at which the superconducting phase disappears is remarkably smal…
We use a holographic theory to model and study the competition of four phases: an antiferromagnetic phase, a superconducting phase, a metallic phase and a striped phase, using as control parameters temperature and a doping-like parameter. We analyse the various instabilities and determine the possible phases. One class of phase diagrams, that we analyse in detail, is similar to that of high-temperature superconductors as well as other strange metal materials.
We construct a holographic SU(2) p-wave superconductor model with Weyl corrections. The high derivative (HD) terms do not seem to spoil the generation of the p-wave superconducting phase. We mainly study the properties of AC conductivity, which is absent in holographic SU(2) p-wave superconductor with Weyl corrections. The conductivities in superconducting phase exhibit obvious anisotropic behaviors. Along $y$ direction, the conductivity $σ_{yy}$ is similar to that of holographic s-wave superconductor. The superconducting energy gap exhibits a wide extension. For the conductivity $σ_{xx}$ alon…
The holographic approach to study strongly coupled superconductors in the presence of dark matter is reviewed. We discuss the influence of dark matter on the superconducting transition temperature of both s-wave and p-wave holographic superconductors. The upper critical field, coherence length, penetration depth of holographic superconductors as well as the metal-insulator transitions have also been analysed. Issues related to the validity of AdS/CFT correspondence for the description of superconductors studied in the laboratory and possible experiments directed towards the detection of dark m…
Holographic superconductivity of a critical Fermi surface
本文研究了二维金属在铁磁量子临界点处的三重态超导性，通过全息方法推导了配对问题，并揭示了AdS₂⊗R₂几何结构对量子临界配对的影响。
We construct a holographic superconductor model, based on a gravity theory, which exhibits novel metal-insulator transitions. We investigate the condition for the condensation of the scalar field over the parameter space, and then focus on the superconductivity over the insulating phase with a hard gap, which is supposed to be Mott-like. It turns out that the formation of the hard gap in the insulating phase benefits the superconductivity. This phenomenon is analogous to the fact that the pseudogap phase can promote the pre-pairing of electrons in high $T_c$ cuprates. We expect that this work …
The difficulty of describing the gauge dependent bi-quark condensate in the QCD colour superconducting phase has made it hard to construct a holographic dual of the state. To side step this problem, we argue that near the chiral restoration transition in the temperature-chemical potential plane, the strongly coupled gluons are likely completely gapped so that the colour quantum numbers of the quarks can be thought of below that gap as global indices. A standard AdS-superconductor model can then be used to analyze the fermionic gap formation. We investigate the role of four-fermion interactions…
We study a generalization of the standard holographic p-wave superconductor featuring two interacting vector order parameters. Basing our argument on the symmetry and linear response properties of the model, we propose it as a holographic effective theory describing a strongly coupled ferromagnetic superconductor. We show that the two order parameters undergo concomitant condensations as a manifestation of an intrinsically interlaced electric/magnetic dynamics. Such intertwined dynamics is confirmed by the study of the transport properties. We characterize thoroughly the equilibrium and the li…
We study Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. We show that supersymmetric solutions are in one-to-one correspondence with solutions to a set of differential constraints on an SU(2) structure. As an application of our results we (i) show that this structure reduces at a conformal boundary to the five-dimensional rigid supersymmetric geometry previously studied by the authors, (ii) find a general expression for the holographic dual of the VEV of a BPS Wilson loop, matching an exact field theory computation, (iii) construct holographic…
We study the fermionic spectral function in a holographic superconductor model. At zero temperature, the black hole has zero horizon and hence the entropy of the system is zero after the back reaction of the condensate is taken into account. We find the system exhibits the famous peak-dip-hump lineshape with a sharp low-energy peak followed by a dip then a hump at higher energies. This feature is widely observed in the spectrum of several high-T_c superconductors. We also find a linear relation between the gap in the fermionic spectrum and the condensate, indicating the condensate is formed by…
By combining a holographic p-wave superconductor model and a holographic ferromagnetism model, we study the coexistence and competition of ferromagnetism and p-wave superconductivity. It is found that the results depend on the self-interaction of magnetic moment of the complex vector field and which phase appears first. In the case that the ferromagnetic phase appears first, if the interaction is attractive, the system shows the ferromagnetism and superconductivity can coexist in low temperatures. If the interaction is repulsive, the system will only be in a pure ferromagnetic state. In the ca…
We construct a toy model for holographic superconductor with non linear Maxwell field in the frame of modified gravity. By probe the bulk background by non linear Maxwell fields we show that superconductivity happens under a specific critical temperature. The effect of the non linear Maxwell field and non linear curvature corrections have been studied by analytical matching methods. We conclude that the non linearity in Maxwell field and curvature coupling make condensation harder.
We study the one dimensional s-wave holographic superconductor by turning on the vector potential $A_x$ in the bulk, which behaves as $A_x=A_x^{(0)} \ln z+ A_x^{(1)}$ on the boundary. By solving the model with fixed $A_x^{(0)}$, we find that if we identify the $A_x^{(0)}$ with the supercurrent $j_x$ of the holographic superconductor, the results agree with the Gindzburg- Landau theory. For example, $A_x^{(0)}$ will break the superconductivity, and the critical value of $A_x^{(0)}$ is proportional to $(T_c-T)^{3/2}$.
Studying the color superconductivity (CSC) phase is essential to understand the physics in the core of the neutron stars which is the only known context where the CSC phase might appear due to the gravitational force squeezing the matter to a sufficiently high density. We propose a simple holographic dual description of the CSC phase transition in the realistic Yang-Mills theory with the power-law Maxwell field. We find the CSC phase transition with the large color number in the deconfinement phase, which is not found in the case of the usual Maxwell field, if the power parameter characterizin…
We construct a $6$ derivative holographic superconductor model in the $4$-dimensional bulk spacetimes, in which the normal state describes a quantum critical (QC) phase. The phase diagram $(γ_1,\hat{T}_c)$ and the condensation as the function of temperature are worked out numerically. We observe that with the decrease of the coupling parameter $γ_1$, the critical temperature $\hat{T}_c$ decreases and the formation of charged scalar hair becomes harder. We also calculate the optical conductivity. An appealing characteristic is a wider extension of the superconducting energy gap, comparing with …
In these lecture notes we derive a generic holographic string theory realization of a p-wave superconductor and superfluid. For this purpose we also review basic D-brane physics, gauge/gravity methods at finite temperature, key concepts of superconductivity and recent progress in distinct realizations of holographic superconductors and superfluids. Then we focus on a D3/D7-brane construction yielding a superconducting or superfluid vector-condensate. The corresponding gauge theory is 3+1-dimensional N=2 supersymmetric Yang-Mills theory with SU(N) color and SU(2) flavor symmetry. It shows a sec…
Holographic SU(3) color superconductivity at finite baryon chemical potential
该研究构建有限重子化学势下的SU(3)色超导电性全息模型，分析μ_b对s、p波的相反影响，揭示S+相随μ_b增大占据色超导区域，为致密QCD和中子星物理提供新视角。
We build a holographic superconductor model with a scalar triplet charged under an SU(2) gauge field in the bulk. In this model, the s-wave and p-wave condensates can be consistently realized. We find that there are totally four phases in this model, namely, the normal phase without any condensate, s-wave phase, p-wave phase and the s+p coexisting phase. By calculating Gibbs free energy, the s+p coexisting phase turns out to be thermodynamically favored once it can appear. The phase diagram with the dimension of the scalar operator and temperature is drawn. The temperature range for the s+p co…
We present a holographic model of QCD with a first order chiral restoration phase transition with chemical potential, mu. The first order behaviour follows from allowing a discontinuity in the dual description as the quarks are integrated out below their constituent mass. The model predicts a deconfined yet massive quark phase at intermediate densities (350 MeV< mu <500 MeV), above the nuclear density phase, which has a very stiff equation of state and a speed of sound close to one. We also include a holographic description of a colour superconducting condensate in the chirally restored vacuum…
Superconductivity from D3/D7: Holographic Pion Superfluid
我们证明了一个D3/D 7系统（零夸克质量极限）在有限的同位旋化学势下经历一个类似超导（超流体）的相变。这类似于QCD文献中研究的调味超流相，其中介子算子凝聚。我们研究了凝聚体的电导率随频率的变化，发现在零频率极限处有一个δ函数极点。这是弦论中超导性的一个例子。因此，我们已经找到了一个超流/超流型的解决方案，并研究了相关的相图。在临界超流速度下，超导转变从二阶转变为一阶。我们已经研究了超导系统的各种性质，如超流密度，能隙，第二声等。我们调查的可能性，同位旋化学势修改嵌入的味膜检查是否横向标量也凝聚在低温下。然而，情况似乎并非如此。
A review on the equation of state of color superconductivity via holography
本文通过全息方法研究了Einstein-Gauss-Bonnet引力中彩色超导相的方程状态，探讨了去 confinement 和 confinement 阶段的相变特性。
Understanding the role of charge density wave (CDW) in high-temperature superconductivity is a longstanding challenge in condensed matter physics. We construct a holographic superconductor model in which the $U(1)$ symmetry is spontaneously broken only due to the presence of CDWs, rather than previously known free charges with constant density. Below the critical temperature of superconductivity, CDW phase and superconducting phase coexist, which is also justified by the numerical results of optical conductivity. The competitive and cooperative relations between CDW phase and superconducting p…
Superconductivity is abundant near quantum-critical points, where fluctuations suppress the formation of Fermi liquid quasiparticles and the BCS theory no longer applies. Two very distinct approaches have been developed to address this issue: quantum-critical Eliashberg theory and holographic superconductivity. The former includes a strongly retarded pairing interaction of ill-defined fermions, the latter is rooted in the duality of quantum field theory and gravity theory. We demonstrate that both are different perspectives of the same theory. We derive holographic superconductivity in form of…
Vortex-Antivortex Lattices in a Holographic Superconductor
本文利用爱因斯坦-阿贝尔-希格斯理论，研究空间周期磁场下超导体中的涡旋-反涡旋晶格结构，通过调节磁场周期和振幅观测到多种涡旋态，并绘制相图以划分各态区域。
It is known that a classical SU(2) Einstein-Yang-Mills theory in 3+1 dimensional anti-de Sitter spacetime can provide a holographic dual to a 2+1 dimensional time reversal symmetry breaking superconductor with a pseudogap. We study the properties of this holographic superconductor in the presence of an applied constant external magnetic field, neglecting backreaction on the geometry. The superconductor is immersed into a constant external magnetic field by adding a radially (the extra dimension) dependent magnetic field to the black hole. As for real superconductors, there is a critical magnet…
Towards holographic color superconductivity in QCD
通过引入带电标量场描述解禁闭相中夸克对的凝聚，扩展全息V-QCD模型，得到了包含一级解禁闭相变及其临界端点以及二级配对-非配对夸克物质相变的相图，并发现均匀配对相的生长速率低于调制相。
Building a "holographic dual" to QCD in the AdS$_5$: instantons and confinement
最近试图找到一个"全息对偶“的QCD类理论包括一个建议，由卡什等人（以下简称为KKSS），以纳入限制通过一个潜在的平方增加到第5个方向的$AdS_5$空间。我们表明，从完全不同的论证路线得出同样的结论。如果通过在第5个坐标处识别瞬子大小$ρ$将瞬子提升到5d空间中，则背景几何必须是AdS $_5$。正如我在1999年已经论证过的，通过"双超导性“描述的约束导致了一个因子$exp(-2πσρ^2)$，其中$σ$是弦张力，这几乎与KKSS提出的完全相同。该表达式也得到了可用晶格数据的很好支持。在文章的最后，我们提出了一个推广到非零温度的IR势。
A study of layered holographic superconductor
本文基于AdS/CFT对偶构建(2+1)维多层全息超导体模型，揭示有限尺寸、层数与层间距对临界温度和临界磁场的影响，并刻画密堆积多层极限下的2D到3D行为转变。
Motivated by the recent use of certain consistent truncations of M-theory to study condensed matter physics using holographic techniques, we study the SU(3)-invariant sector of four-dimensional, N=8 gauged supergravity and compute the complete scalar spectrum at each of the five non-trivial critical points. We demonstrate that the smaller SU(4)^- sector is equivalent to a consistent truncation studied recently by various authors and find that the critical point in this sector, which has been proposed as the ground state of a holographic superconductor, is unstable due to a family of scalars th…
Within gauge/gravity duality, we consider finite density systems in a helical lattice dual to asymptotically anti-de Sitter space-times with Bianchi VII symmetry. These systems can become an anisotropic insulator in one direction while retaining metallic behavior in others. To this model, we add a $U(1)$ charged scalar and show that below a critical temperature, it forms a spatially homogeneous condensate that restores isotropy in a new superconducting ground state. We determine the phase diagram in terms of the helix parameters and perform a stability analysis on its IR fixed point correspond…
We consider charged rotating BTZ black holes in 2+1 dimensions and obtain 1+1 dimensional holographic superconductors on a spatial circle in the context of the $AdS_3/CFT_2$ correspondence. The charged condensate for the boundary superconductor is computed both in the analytic and the numerical framework in a probe limit and a low angular momentum approximation. A critical value of the angular momentum for the onset of superconductivity is established. We also numerically compute the electrical conductivity of the 1+1 dimensional boundary theory on a circle. The conductivity exhibits a depende…
In this paper, we have constructed a bottom-up holographic model for the color superconductivity (CSC) of the Yang-Mills theory with including the higher derivative corrections which allow to study the CSC phase with the color number $N_c\geq2$. First, we consider the CSC phase transition in the context of Einstein-Gauss-Bonnet (EGB) gravity. We analyze the Cooper pair condensate in the deconfinement and confinement phases which are dual to the planar GB-RN-AdS black hole and GB-AdS soliton, respectively, where the backreaction of the matter part is taken into account. By examining the breakdo…
A Holographic Superconductor in an External Magnetic Field
在3+1维反de Sitter时空中，研究了一个与Reissner-Nordstrom黑洞耦合的复杂带电标量系统，忽略了反作用.在适当的边界条件下，中性和纯电黑洞的情况在不同的极限下进行了研究，并表明在双2+1维场论中产生超导性的关键元素，在临界温度以下形成凝聚。通过在黑洞中加入磁荷，我们将超导体浸入外部磁场中。我们表明，一个家庭的凝聚物可以形成，我们检查他们的结构。对于有限的磁场，他们是本地化在一个维度上的轮廓，是完全可解的，因为它映射到量子谐振子。随着磁场的增加，凝聚体的尺寸会缩小，这让人联想到迈斯纳效应。
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