We implement the momentum dissipation introduced by spatial linear axionic fields in a holographic model without self-duality, broke by Weyl tensor coupling to Maxwell field, and study its response. It is found that for the positive Weyl coupling parameter $γ>0$, the momentum dissipation characterized by parameter $\hatα$ drives the boundary conformal field theory (CFT), in which the conductivity exhibits a peak at low frequency, into the incoherent metallic phase with a dip, which is away from CFT due to the introduction of axionic fields. While for $γ<0$, an oppositive scenario is found. Our present model provides a possible route toward the problem that which sign of $γ$ is the correct description of the CFT of boson Hubbard model. In addition, we also investigate the DC conductivity, diffusion constant and susceptibility. We find that for each of these observables there is a specific value of $\hatα$, for which these observables are independent of $γ$. Finally, the electromagnetic (EM) duality is also studied and we find that there is also a specific value of $\hatα$, for which the particle-vortex duality related by the change of the sign of $γ$ in the boundary theory holds better than for other values of $\hatα$.
The unusual magnetic materials are significant in both science and technology. However, because of the strongly correlated effects, it is difficult to understand their novel properties from theoretical aspects. Holographic duality offers a new approach to understanding such systems from gravity side. This paper will give a brief review of our recent works on the applications of holographic duality in understanding unusual magnetic materials. Some quantitative compare between holographic results and experimental data will be shown and some predictions from holographic duality models will be dis…
In this paper, we obtain a holographic model of dark energy using the fluid/gravity duality. This model will be dual to a higher dimensional Schwarzschild black hole, and we would use fluid/gravity duality to relate to the parameters of this black hole to such a cosmological model. We will also analyze the thermodynamics of such a solution, and discuss the stability model. Finally, we use cosmological data to constraint the parametric space of this dark energy model. Thus, we will use observational data to perform cosmography for this holographic model based on fluid/gravity duality.
Self-duality in Euclidean gravitational set ups is a tool for finding remarkable geometries in four dimensions. From a holographic perspective, self-duality sets an algebraic relationship between two a priori independent boundary data: the boundary energy-momentum tensor and the boundary Cotton tensor. This relationship, which can be viewed as resulting from a topological mass term for gravity boundary dynamics, survives under the Lorentzian signature and provides a tool for generating exact bulk Einstein spaces carrying, among others, nut charge. In turn, the holographic analysis exhibits per…
We construct a higher derivative theory involving an axionic field and the Weyl tensor in four dimensional spacetime. Up to the first order of the coupling parameters, the charged black brane solution with momentum dissipation in a perturbative manner is constructed. Metal-insulator transitions are implemented when varying the system parameters at zero temperature. Also, we study the transports including DC conductivity and optical conductivity at zero charge density. We observe the exact particle-vortex duality for some specific momentum dissipation strength.
We investigate background metrics for 2+1-dimensional holographic theories where the equilibrium solution behaves as a perfect fluid, and admits thus a thermodynamic description. We introduce stationary perfect-Cotton geometries, where the Cotton--York tensor takes the form of the energy--momentum tensor of a perfect fluid, i.e. they are of Petrov type D_t. Fluids in equilibrium in such boundary geometries have non-trivial vorticity. The corresponding bulk can be exactly reconstructed to obtain 3+1-dimensional stationary black-hole solutions with no naked singularities for appropriate values o…
We construct a generalized Smarr formula which could provide a thermodynamic route to derive the covariant field equation of general theories of gravity in dynamic spacetimes. Combining some thermodynamic variables and a new chemical potential conjugated to the number of degree of freedom on the holographic screen, we find a universal Cardy-Verlinde formula and give its braneworld interpretation. We demonstrate that the associated AdS-Bekenstein bound is tighten than the previous expression for multi-charge black holes in the gauged supergravities. The Cardy-Verlinde formula and the AdS-Bekens…
We prove several universal properties of charge transport in generic CFTs holographic to nonminimal extensions of four-dimensional Einstein-Maxwell theory with exact electromagnetic duality invariance. First, we explicitly verify that the conductivity of these theories at zero momentum is a universal frequency-independent constant. Then, we derive their analytical expressions for non-zero momentum in any holographic duality-invariant theory for large frequencies and in the limit of small frequencies and momenta. Next, in the absence of terms that couple covariant derivatives of the curvature t…
Duality and four-dimensional black holes: gravitational waves, algebraically special solutions, pole skipping, and the spectral duality relation in holographic thermal CFTs
In this paper, we use Born-Infeld black holes to test two recent holographic conjectures of complexity, the "Complexity = Action" (CA) duality and "Complexity = Volume 2.0" (CV) duality. The complexity of a boundary state is identified with the action of the Wheeler-deWitt patch in CA duality, while this complexity is identified with the spacetime volume of the WdW patch in CV duality. In particular, we check whether the Born-Infeld black holes violate the Lloyd bound: $\mathcal{\dot{C}\leq}\frac{2}{π\hbar}\left[ \left( M-QΦ\right) -\left( M-QΦ\right) _{\text{gs}}\right] $, where gs stands for…
We classify the different phases by the "pole-zero mechanism" for a holographic fermionic system which contains a dipole coupling with strength $p$ on a Q-lattice background. A complete phase structure in $p$ space can be depicted in terms of Fermi liquid, non-Fermi liquid, Mott phase and pseudo-gap phase. In particular, we find that in general the region of the pseudo-gap phase in $p$ space is suppressed when the Q-lattice background is dual to a deep insulating phase, while for an anisotropic background, we have an anisotropic region for the pseudo-gap phase in $p$ space as well. In addition…
Quantum information theory along with holography play central roles in our understanding of quantum gravity. Exploring their connections will lead to profound impacts on our understanding of the modern physics and is thus a key challenge for present theory and experiments. In this paper, we investigate a recent conjectured connection between reduced fidelity susceptibility and holographic complexity (the RFS/HC duality for short). We give a quantitative proof of the duality by performing both holographic and field theoretical computations. In addition, holographic complexity in $AdS_{2+1}$ are…
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 construct a holographic effective superconducting theory by considering a special gauge-axion higher derivative term. The gauge-axion coupling results in the transport behavior similar to the vortex response in the dual boundary field theory leading to non-Drude behavior of alternating current (AC) conductivity at the weak momentum dissipation. With the momentum dissipation increasing, a dip exhibits in the AC conductivity at low frequency. It is thought to be the result of a combination of the strong momentum dissipation and the gauge-axion coupling. In the superconducting phase, this gaug…
We extend the holographic duality between 3d pure gravity and the 2d Ising CFT proposed in [Phys. Rev. D 85 (2012) 024032] to CFTs with boundaries. Besides the usual asymptotic boundary, the dual bulk spacetime now has a real cutoff, on which live branes with finite tension, giving Neumann boundary condition on the metric tensor. The strongly coupled bulk theory requires that we dress the well-known semiclassical AdS/BCFT answer with boundary gravitons, turning the partition function into the form of Virasoro characters. Using this duality, we relate the brane tensions to the modular S-matrix …
We perform the resummation of the infrared logarithms in the inflationary universe. Applying the renormalization group, we derive the stochastic equations as the effective theory at the horizon. We focus on the conformal zero mode to respect local Lorentz symmetry. Under Gaussian approximation, we derive the fundamental equation for the Universe (EqU). We also derive the identical equation from the first law of thermodynamics in a dual geometric picture. We believe it is a convincing evidence for de Sitter duality between quantum stochastic physics on the boundary and classical thermodynamics …
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 employ holographic duality to compute $\langle T_{μν} \rangle$ in strongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills theory and then study evolution of the semiclassical Einstein field equations sourced by $\langle T_{μν} \rangle$. Linearizing about de Sitter space, we find that the semiclassical equations of motion reduce to a four dimensional scalar wave equation coupled to a five dimensional scalar wave equation. We compute the mode spectrum of these equations and find that there exists a critical value of the Hubble constant $H_c$ for which de Sitter space is unstable when $H <…
We find new type II backgrounds with non-relativistic symmetries via non-Abelian T-duality. First we consider geometries with Galilean symmetries in type IIA, which have been identified as non-relativistic generalizations of the ABJM background and massive IIA supergravities. We then consider the non-Abelian T-duality transformation on the backgrounds with Lifshitz symmetry constructed by Donos and Gauntlett. Using gauge/gravity duality we study aspects of the field theory dual to these backgrounds.
A real anti-symmetric tensor field was introduced to realize a holographic magnetic ordered phase in our previous works. However, a more careful analysis shows there is a vector ghost in the model. In this paper we present a modified Lagrangian density for the anti-symmetric tensor, which is ghost free and causality is well-defined, and keeps all the significant results in the original model qualitatively. We show this modified Lagrangian density could come from the dimensional compactification of $p$-form field in String/M-theory. For static curved space-time, we also prove that this modified…
We develop analytic techniques to construct the leading dissipative terms in a derivative expansion of holographic fluids. Our basic ingredient is the Crnkovic-Witten symplectic current of classical gravity which we use to extract the dissipative transport coefficients of holographic fluids, assuming knowledge of the thermodynamics and the near horizon geometries of the bulk black hole geometries. We apply our techniques to non-conformal neutral fluids to reproduce previous results on the shear viscosity and generalise a known expression for the bulk viscosity.
We systematically present a new approach for studying the coupled linear transport of holographic systems. In this approach, the set of equations for the linear perturbations can be reduced to a first-order nonlinear ordinary differential equation expressed as the radial (renormalization group) flow equation of the transport matrices. As an important application, we use this approach to compute the DC and AC conductivities of a holographic model with momentum dissipation, which can be easily read off from the nonlinear flow equations. This method also works for transport in the presence of an …
The area law of Bekenstein-Hawking entropy of the black hole suggests that the black hole should have a lower-dimensional holographic description. It has been found recently that such holographic pictures could be set up from the study of the thermodynamics of both outer and inner horizons for a large class of rotating and charged black holes. For a four-dimensional dyonic Reissner-Nordström black hole, its thermodynamics indicates that it has multiple holographic pictures not only the electric and magnetic ones corresponding to the conserved electric and magnetic charges carried by the black …
The holographic renormalization group (RG) flows in certain self-dual two dimensional QFT's models are studied. They are constructed as holographic duals to specific New Massive 3d Gravity (NMG) models coupled to scalar matter with "partially self-dual" superpotentials. The standard holographic RG constructions allow us to derive the exact form of their $β$- functions in terms of the corresponding NMG's domain walls solutions. By imposing invariance of the free energy, the central function and of the anomalous dimensions under specific matter field's duality transformation, we have found the c…
We establish a precise relation between mixed boundary conditions for scalar fields in asymptotically anti de Sitter spacetimes and the equation of state of the dual fluid. We provide a detailed derivation of the relation in the case of five bulk-dimensions for scalar fields saturating the Breitenlohner-Freedman bound. As a concrete example, we discuss the five dimensional scalar-tensor theories describing a constant speed of sound.
These are notes from my lectures at TASI 2015. The goal is to provide context for the study of strongly-correlated quantum many-body systems using quantum field theory, and possibly string theory.
In this paper we review some results on the generalization of the gauge/gravity duality to include fundamental matter by means of probe branes. We compute the meson spectrum of maximally supersymmetric gauge theories in several dimensions, both in the Coulomb and Higgs branch. We also study the addition of flavor and compute the meson spectrum for non-commutative theories. Additionally, we present a thorough search of supersymmetric embeddings of probe branes in the Klebanov-Witten model.
According to the holographic principle, the description of a volume of space can be thought of as encoded on its boundary. Holographic principle establishes equivalence, or duality, between theoretical description of volume physics, which involves gravity, and the gravity-free field theory, which describes physics on its surface. While generally accepted as a theoretical framework, so far there was no known experimental system which would exhibit explicit holographic duality and be amenable to direct experimental testing. Here we demonstrate that nonlinear optics of hyperbolic metamaterials ad…
We study dissipation in holographic superfluids at finite temperature and zero chemical potential. The zero overlap with the heat current allows us to isolate the physics of the conserved current corresponding to the broken global $U(1)$. By using analytic techniques we write constitutive relations including the first non-trivial dissipative terms. The corresponding transport coefficients are determined in terms of thermodynamic quantities and the black hole horizon data. By analysing their behaviour close to the phase transition we show explicitly the breakdown of the hydrodynamic expansion. …
We introduce the gauge/gravity, or AdS/CFT, correspondence with an eye towards its application to strongly coupled systems. We provide an overview of the duality, including the AdS/CFT dictionary and holographic renormalization. We then discuss simple correlation functions in the context of renormalization group flow geometries, holographic thermodynamics and an application to the phase diagram of QCD, real-time correlators and the shear viscosity of strongly coupled field theories, holographic superconductors, and the application of holographic fermionic response to strange metals. These lect…
We show that the quantum entanglement can be transmuted to a force using the holographic duality. First, we prove that there is an open string in the spectrum of the holographic fermion coupled with scalar. The string ends at two fermions and its tension vanishes in the limit of zero scalar condensation. We associate such string with a dimer and identify the scalar condensation as the degree of the dimerization. Together with divergently large entanglement entropy, the model is expected to describe the Spin Liquid. As a consistency check, we show that there is a Mott transition as the dimeriza…
We review warped compactifications of superstring theory with some attention to the limit in which these resemble "bottom-up" phenomenological models. In addition to some discussion of the original Klebanov-Witten and Klebanov-Strassler set-ups, we also touch on various generalizations of the geometry that have been considered. Various other systems with a holographic duality are also briefly reviewed. The point of this latter exploration is to illustrate how far beyond the standard AdS(5) x S(5) set-up things have moved over the years.
In this Letter, based on the notion of gauge/gravity duality, we compute $ q $ SYK spectra in the presence of Yang-Baxter (YB) deformations. The gravitational counterpart of this duality turns out to be the YB deformed Almheiri-Polchinski (AP) model embodied with hyperbolic potential for the dilaton. Following Kaluza-Klein reduction on $ (AdS_2)_η\times (S^1/ Z_2) $, we compute the deformed Green's function that reproduces the original $ q $ SYK spectrum in the limit of vanishing deformations.
These lectures give an introduction to the theory of holographic superconductors. These are superconductors that have a dual gravitational description using gauge/gravity duality. After introducing a suitable gravitational theory, we discuss its properties in various regimes: the probe limit, the effects of backreaction, the zero temperature limit, and the addition of magnetic fields. Using the gauge/gravity dictionary, these properties reproduce many of the standard features of superconductors. Some familiarity with gauge/gravity duality is assumed. A list of open problems is included at the …
Ultraviolet dissipation and defect OPE in bottom-up holographic interfaces
Weinberg Institute for Theoretical Physics, The University of Texas at Austin（德克萨斯大学奥斯汀分校温伯格理论物理研究所）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo（东京大学 Kavli宇宙物理与数学研究所（WPI），东京大学高等研究院）
In the AdS/CFT duality, it is often said that a local symmetry in a bulk theory corresponds to a global symmetry in the corresponding boundary theory, but the global symmetry can become local when one couples with an external source. As a result, the GKP-Witten relation gives a response function instead of a Green function. We explore this point in details using the example of holographic superconductors. We point out that these points play a crucial role to interpret the holographic London equation properly.
We study the conductivity from higher derivative electrodynamics in a holographic quantum critical phase (QCP). Two key features of this model are observed. First, a rescaling for the Euclidean frequency by a constant is needed when fitting the quantum Monte Carlo (QMC) data for the $O(2)$ QCP. We conclude that it is a common characteristic of the higher derivative electrodynamics. Second, both the Drude-like peak at low frequency and the pronounced peak can simultaneously emerge. They are more evident for the relevant operators than for the irrelevant operators. In addition, our result also f…
We study minimal co-dimension-2 surfaces in the asymptotically flat background of extremal 3-brane solutions in ten-dimensional type IIB supergravity. A conjectured open-closed string duality combined with the Ryu-Takayanagi prescription implies that the area of the surfaces we consider could be interpreted as the entanglement entropy of a dual (3+1)-dimensional large-N, strongly-coupled open string field theory on D3-branes. As the size of the surface is varied we observe a transition from a volume law to an area law in agreement with expectations from non-locality in an open string field the…
We study the Hawking-Page transition in a holographic model of field theories with momentum dissipation. We find that the deconfinement temperature strictly decreases as momentum dissipation is increased. For sufficiently strong momentum dissipation, the critical temperature goes to zero, indicating a zero-temperature deconfinement transition in the dual field theory.
We present a strange metal, described by a holographic duality, which reproduces the famous linear resistivity of the normal state of the copper oxides, in addition to the linear specific heat. This holographic metal reveals a simple and general mechanism for producing such a resistivity, which requires only quenched disorder and a strongly interacting, locally quantum critical state. The key is the minimal viscosity of the latter: unlike in a Fermi-liquid, the viscosity is very small and therefore is important for the electrical transport. This mechanism produces a resistivity proportional to…
The gauge-gravity duality and analog gravity both relate a condensed matter system to a gravitational theory. This makes it possible to use gravity as an intermediary to establish a relation between two different condensed matter systems: The strongly coupled system from the gauge-gravity duality and the weakly coupled gravitational analog.We here offer some examples for relations between observables in the two different condensed matter systems. In particular, we show that in some cases Green's functions and first order transport coefficients in holographic models are of the same form as thos…
The AdS/CFT correspondence realises the holographic principle where information in the bulk of a space is encoded at its border. We are yet a long way from a full mathematical construction of AdS/CFT, but toy models in the form of holographic quantum error correcting codes (HQECC) have replicated some interesting features of the correspondence. In this work we construct new HQECCs built from random stabilizer tensors that describe a duality between models encompassing local Hamiltonians whilst exactly obeying the Ryu-Takayanagi entropy formula for all boundary regions. We also obtain complemen…
These are notes based on a series of lectures given at the KITP workshop "Quantum Criticality and the AdS/CFT Correspondence" in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion of string theory and of supersymmetry is avoided to the extent possible.
In this thesis we review some results on the generalization of the gauge/gravity duality to new cases by using T-duality and by including fundamental matter, finding applications to condensed matter physics. First, we construct new supersymmetric solutions of type IIA/B and eleven-dimensional supergravity by using non-abelian T-duality. Second, we construct a type IIA supergravity solution with D6-brane sources, dual to an unquenched massive flavored version of the ABJM theory. Third, we study a probe D6-brane with worldvolume gauge fields in the ABJM background, obtaining the dual description…
We consider a holographic model with the charge current dual to a general nonlinear electrodynamics (NLED) field. Taking into account the backreaction of the NLED field on the geometry and introducing axionic scalars to generate momentum dissipation, we obtain expressions for DC conductivities with a finite magnetic field. The properties of the in-plane resistance are examined in several NLED models. For Maxwell-Chern-Simons electrodynamics, negative magneto-resistance and Mott-like behavior could appear in some parameter space region. Depending on the sign of the parameters, we expect the NLE…
We study the effects of Gauss-Bonnet corrections on some nonlocal probes (entanglement entropy, $n$-partite information and Wilson loop) in the holographic model with momentum relaxation. Higher-curvature terms as well as scalar fields make in fact nontrivial correction to the coefficient of universal term in entanglement entropy. We use holographic methods to study such corrections. Moreover, holographic calculation indicates that mutual and tripartite information undergo a transition beyond which they identically change their values. We find that the behavior of transition curves depends on …
We study the holographic duality between boundary OPE blocks and geodesic integrated bulk fields in quotients of AdS$_3$ dual to excited CFT states. The quotient geometries exhibit non-minimal geodesics between pairs of spacelike separated boundary points which modify the OPE block duality. We decompose OPE blocks into quotient invariant operators and propose a duality with bulk fields integrated over individual geodesics, minimal or non-minimal. We provide evidence for this relationship by studying the monodromy of asymptotic maps that implement the quotients.
In this work we study a dissipative field theory where the dissipation process is manifestly related to dynamical entanglement and put it in the holographic context. Such endeavour is realized by further development of a canonical approach to study quantum dissipation, which consists of doubling the degrees of freedom of the original system by defining an auxiliary one. A time dependent entanglement entropy for the vacumm state is calculated and a geometrical interpretation of the auxiliary system and the entropy is given in the context of the AdS/CFT correspondence using the Ryu-Takayanagi fo…
In this paper, we study $(2+1)$-dimensional quantum anomalous Hall states, i.e. band insulators with quantized Hall conductance, using the exact holographic mapping. The exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in $(3+1)$-dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a $(3+1)$-dimensional topological insulator. The dual description enables a new characterizat…
We introduce a duality relation between two distinct branes, a cosmological brane with macroscopic matter and a holographic brane with microscopic gauge fields. Using brane-world cosmology with a single brane in a 5-dimensional AdS5 background, we find an explicit time-dependent holographic correspondence between the bulk metric surrounding the cosmological brane and the N=4 gauge field theory living on the boundary of the Z2-symmetric mirror bulk, identified with the holographic brane. We then relate the cosmic acceleration on the cosmological brane to the conformal anomaly of the gauge theor…
A new dynamic SU(3)-structure solution in type-IIA is found by T-dualising a deformation of the Maldacena-Nastase solution along an SU(2) isometry. It is argued that this is dual to a quiver gauge theory with multiple Chern-Simons levels. A clear way of defining Chern-Simons levels in terms of Page charges is presented, which is also used to define a Chern-Simons term for the G2-structure analogue of Klebanov-Strassler, providing evidence of a cascade in both the ranks and levels of the dual quiver.
