The AdS/CFT correspondence has significantly impacted the study of strongly coupled systems, providing insights into various condensed matter phenomena through its holographic duality. This paper introduces an alternative approach to the breaking of the global $U(1)$ symmetry in the bulk in two asymptotically AdS spacetimes: AdS plus hard wall and AdS Blackbrane. We explore a $(3+1)$-dimensional bulk $U(1)$ symmetry-breaking phase vacuum within a global $U(1)$ $ϕ^4$ field theory, without the gauge field present in prior models. We find the symmetry-breaking vacuum requires that the mass squared is proportional to the quartic coupling. We also investigate numerical solutions of topologically stable vortex strings extending into the bulk. We find evidence that the full UV expansion is dual to a point-like boundary excitation.
Gauge invariance plays an important role in forming topological defects. In this work, from the AdS/CFT correspondence, we realize the clusters of equal-sign vortices during the course of critical dynamics of a strongly coupled superconductor. This is the first time to achieve the equal-sign vortex clusters in strongly coupled systems, considering that vortices with equal sign repel. The appearance of clusters of equal-sign vortices is a typical character of flux trapping mechanism, distinct from Kibble-Zurek mechanism which merely presents vortex-antivortex pair distributions resulting from g…
We study black hole solutions of $D=4$ Einstein-Maxwell theory coupled to a charged scalar field that are holographically dual to a $d=3$ conformal field theory with a non-vanishing chemical potential and constant magnetic field. We numerically construct black hole solutions that are dual to a superfluid phase with a periodic lattice of vortices. For the specific model we investigate, we find that the thermodynamically preferred configuration is given by a triangular lattice and moreover the vortices are associated with the lowest Landau level. We also construct black holes describing a lattic…
In this work, we have analytically devised novel vortex solutions in a rotating holographic superfluid. To achieve this result, we have considered a static disc at the AdS boundary and let the superfluid rotate relative to it. This idea has been numerically exploited in [1] where formation of vortices in such a setting was reported. We have found that these vortex solutions are eigenfunctions of angular momentum. We have also shown that vortices with higher winding numbers are associated with higher quantized rotation of the superfluid. We have, then, analysed the equation of motion along bulk…
In a holographic superfluid disk, when the rotational velocity is large enough, we find a giant vortex will form in the center of the system by merging several single charge vortices at some specific rotational velocity, with a phase stratification phenomenon for the order parameter. The formation of a giant vortex can be explained as there is not enough space for a standard vortex lattice. Keep increasing the rotational velocity the giant vortex will disappear and there will be an appearance of a superfluid ring. In the giant vortex region, the number of vortices measured from winding number …
Within the simplest holographic superfluid model and without any ingredients put by hand, it is shown that vortices can be generated when the angular velocity of rotating superfluids exceeds certain critical values, which can be precisely determined by linear perturbation analyses (quasi-normal modes of the bulk AdS black brane). These vortices appear at the edge of the superfluid system first, and then automatically move into the bulk of the system, where they are eventually stabilized into certain vortex lattices. For the case of 18 vortices generated, we find (at least) five different patte…
Traversing a continuous phase transition at a finite rate leads to the breakdown of adiabatic dynamics and the formation of topological defects, as predicted by the celebrated Kibble-Zurek mechanism (KZM). We investigate universal signatures beyond the KZM, by characterizing the distribution of vortices generated in a thermal quench leading to the formation of a holographic superconductor. The full counting statistics of vortices is described by a binomial distribution, in which the mean value is dictated by the KZM and higher-order cumulants share the universal power-law scaling with the quen…
Splitting Dynamics of Multiply Quantized Vortices in Holographic Superfluid of Finite Temperature
Lingnan Normal University（岭南师范学院）；Hunan Normal University（湖南师范大学）；University of Chinese Academy of Sciences（中国科学院大学）；Zhejiang University（浙江大学）；Beijing Normal University（北京师范大学）
By utilizing the AdS/CFT correspondence, we explore the dynamics of strongly coupled superfluid vortices in a disk with constant angular velocity. Each vortex in the vortex lattice is quantized with vorticity one from the direct inspection of their phases. As the angular velocity of the disk is greater than a critical value, the first vortex will be excited as expected from theoretical predictions. The subsequent two and more vortices are also generated by increasingly rotating the disk, resulting in the remarkable step transitions for the angular velocity to excite each individual vortex. Whe…
We study the holographic entanglement entropy in a (d+1)-dimensional boundary quantum field theory at both the zero and finite temperature. The phase diagrams for the holographic entanglement entropy at various temperatures are obtained by solving the entangled surfaces in the different homology. We also verify the Araki-Lieb inequality and illustrate the entanglement plateau.
We discuss a unified framework of dealing with electrically charged, anyonic vortices in 2+1 dimensional spacetimes and extended, anyonic string-like vortices in one higher dimension. We elaborate on two ways of charging these topological objects and point out that in both cases the vortices and strings obey fractional statistics as a consequence of being electrically charged. The statistics of the charged vortices and strings can be obtained from the phase shift of their respective wave-functions under the classic Aharonov-Bohm type experiments. We show that for a manifold with boundary, wher…
We use holography to investigate the dynamics of a vortex-anti-vortex dipole in a strongly coupled superfluid in 2+1 dimensions. The system is evaluated in numerical real-time simulations in order to study the evolution of the vortices as they approach and eventually annihilate each other. A tracking algorithm with sub-plaquette resolution is introduced which permits a high-precision determination of the vortex trajectories. With the increased precision of the trajectories it becomes possible to directly compute the vortex velocities and accelerations. We find that in the holographic superflui…
We investigate the formation of topological defects in the course of a dynamical phase transition with different boundary conditions in a ring from AdS/CFT correspondence. According to the Kibble-Zurek mechanism, quenching the system across the critical point to symmetry-breaking phase will result in topological defects -- winding numbers -- in a compact ring. By setting two different boundary conditions, i.e., Dirichlet and Neumann boundary conditions for the spatial component of the gauge fields in the AdS boundary, we achieve the holographic superfluid and holographic superconductor models,…
In this paper we discuss geodesic Witten diagrams in general holographic conformal field theories with boundary or defect. In boundary or defect conformal field theory, two-point functions are non-trivial and can be decomposed into conformal blocks in two distinct ways; ambient channel decomposition and boundary channel decomposition. In our previous work we only consider two-point functions of same operators. We generalize our previous work to a situation where operators in two-point functions are different. We obtain two distinct decomposition for two-point functions of different operators.
The 3D Maxwell-Chern-Simons theory with planar, single-edged, boundary is considered. It is shown that its holographic reduction on a flat euclidean 2D spacetime is a scalar field theory describing a conserved chiral current, which corresponds to the electric continuity equation. Differently from the theory with planar, double-edged boundary, in this holographic bulk-boundary approach physical quantities like the chiral velocity of the edge excitations depend also on the non-topological Maxwell term.
In arXiv:1601.02634 it was observed that asymptotic boundary conditions play an important role in the study of holographic entanglement beyond AdS/CFT. In particular, the Ryu-Takayanagi proposal must be modified for warped AdS$_3$ (WAdS$_3$) with Dirichlet boundary conditions. In this paper, we consider AdS$_3$ and WAdS$_3$ with Dirichlet-Neumann boundary conditions. The conjectured holographic duals are warped conformal field theories (WCFTs), featuring a Virasoro-Kac-Moody algebra. We provide a holographic calculation of the entanglement entropy and Rényi entropy using AdS$_3$/WCFT and WAdS$…
We compute correlation functions, specifically 1-point and 2-point functions, in holographic boundary conformal field theory (BCFT) using geodesic approximation. The holographic model consists of a massive scalar field coupled to a Karch-Randall brane -- a rigid boundary in the bulk AdS space. Geodesic approximation requires the inclusion of paths reflecting off of this brane, which we show in detail. For the 1-point function, we find agreement between geodesic approximation and the harder $Δ$-exact calculation, and we give a novel derivation of boundary entropy using the result. For the 2-poi…
${\cal N} = 4$ Supersymmetric Yang-Mills (SYM) theory can be defined on a half-space with a variety of boundary conditions preserving scale invariance and half of the original supersymmetry; more general theories with the same symmetry can be obtained by coupling to a 3D SCFT at the boundary. Each of these theories is characterized by a quantity called "boundary $F$", conjectured to decrease under boundary renormalization group flows. In this paper, we calculate boundary $F$ for $U(N)$ ${\cal N} = 4$ SYM theory with the most general half-supersymmetric boundary conditions arising from string t…
In holographic duality, if a boundary state has a geometric description that realizes the Ryu-Takayanagi proposal then its entanglement entropies must obey certain inequalities that together define the so-called holographic entropy cone. A large family of such inequalities have been proven under the assumption that the bulk geometry is static, using a method involving contraction maps. By using kinematic space techniques, we show that in two boundary (three bulk) dimensions, all entropy inequalities that can be proven in the static case by contraction maps must also hold in holographic states …
The holographic complexity conjectures are considered in a Einstein-Maxwell-Dilaton gravity, by using the "Complexity-Volume" proposal. Specifically, we calculate the growth rate of complexity for an eternal charged AdS-dilaton black holes with fixed and dynamical boundaries respectively. The dynamical boundary is achieved by introducing a moving self-graviting brane on which the induced metric has an exact FLRW form. In case of fixed AdS boundary, there exists a bound for evolution of growth rate on late time, while this bound will become larger as the dilaton coupling constant $α$ increases.…
The holographic principle, being a generic feature of quantum gravity, should allow for the consideration of dualities other than AdS/CFT. The AdS/BCFT correspondence, in which the dual field theory has local conformal symmetry and is defined on a manifold with boundary, is one such example. Inspired by the quotienting of AdS$_3$ by spacetime isometries in order to construct multiboundary wormholes dual to multipartite CFT$_2$ states, we find that this correspondence can be understood by combining AdS/CFT with some appropriate quotient procedure. Furthermore, in three bulk dimensions, we find …
In this paper we propose a space-time random tensor network approach for understanding holographic duality. Using tensor networks with random link projections, we define boundary theories with interesting holographic properties, such as the Renyi entropies satisfying the covariant Hubeny-Rangamani-Takayanagi formula, and operator correspondence with local reconstruction properties. We also investigate the unitarity of boundary theory in spacetime geometries with Lorenzian signature. Compared with the spatial random tensor networks, the space-time generalization does not require a particular ti…
We investigate the duality conjecture "Complexity=Action" (CA) for Born-Infeld (BI) gravity model and derive the growth rate of its action within the Wheeler-DeWitt (WDW) patch, which is believed to be dual to the growth rate of quantum complexity of holographic boundary state. In order to find the correct on-shell action, we use direct variational procedure to find proper boundary and corner terms. We find out that the late-time behavior of holographic complexity is the well-known two times of energy, as expected.
