Quantum critical transport, duality, and M theory

Physical Review D

We discuss the zeroes and poles of the determinant of the retarded Green function ($\det G_R$) at zero frequency in a holographic system of charged massless fermions interacting via a dipole coupling. For large negative values of the dipole coupling constant $p$, $\det G_R$ possesses only poles pointing to a Fermi liquid phase. We show that a duality exists relating systems of opposite $p$. This maps poles of $\det G_R$ at large negative $p$ to zeroes of $\det G_R$ at large positive $p$, indicating that the latter corresponds to a Mott insulator phase. This duality suggests that the properties of a Mott insulator can be studied by mapping the system to a Fermi liquid. Finally, for small values of $p$, $\det G_R$ contains both poles and zeroes (pseudo-gap phase).

International Journal of Modern Physics A, 2012

Using a holographic proposal for the geometric entropy we study its behavior in the geometry of Schwarzschild black holes in global AdS p for p = 3, 4, 5. Holographically, the entropy is determined by a minimal surface. On the gravity side, due to the presence of a horizon on the background, generically there are two solutions to the surfaces determining the entanglement entropy. In the case of AdS 3 , the calculation reproduces precisely the geometric entropy of an interval of length l in a two dimensional conformal field theory with periodic boundary conditions. We demonstrate that in the cases of AdS 4 and AdS 5 the sign of the difference of the geometric entropies changes, signaling a transition. Euclideanization implies that various embedding of the holographic surface are possible. We study some of them and find that the transitions are ubiquitous. In particular, our analysis renders a very intricate phase space, showing, for some ranges of the temperature, up to three branches. We observe a remarkable universality in the type of results we obtain from AdS 4 and AdS 5 .

International Journal of Modern Physics A, 2009

Using a holographic proposal for the entanglement entropy we study its behavior in various supergravity backgrounds. We are particularly interested in the possibility of using the entanglement entropy as way to detect transitions induced by the presence horizons. We consider several geometries with horizons: the black hole in AdS 3 , nonextremal Dp-branes, dyonic black holes asymptotically to AdS 4 and also Schwarzschild black holes in global AdS p coordinates.

Journal of High Energy Physics, 2009

We study four dimensional gravity with a negative cosmological constant deformed by the Nieh-Yan torsional topological invariant with a spacetime-dependent coefficient. We find an exact solution of the Euclidean system, which we call the torsion vortex, having two asymptotic AdS 4 regimes supported by a pseudoscalar with a kink profile. We propose that the torsion vortex is the holographic dual of a three dimensional system that exhibits distinct parity breaking vacua. The torsion vortex represents a (holographic) transition between these distinct vacua. We expect that from the boundary point of view, the torsion vortex represents a 'domain wall' between the two distinct vacua.

Journal of High Energy Physics, 2008

We consider situations where the renormalized geometric entropy, as defined by the AdS/CFT ansatz of Ryu and Takayanagi, shows extensive behavior in the volume of the entangled region. In general, any holographic geometry that is 'capped' in the infrared region is a candidate for extensivity provided the growth of minimal surfaces saturates at the capping region, and the induced metric at the 'cap' is non-degenerate. Extensivity is well-known to occur for highly thermalized states. In this note, we show that the holographic ansatz predicts the persistence of the extensivity down to vanishing temperature, for the particular case of conformal field theories in 2 + 1 dimensions with a magnetic field and/or electric charge condensates.

Physical Review D, 2013

We present a simple analytic gravitational solution which describes the holographic dual of a 2 + 1-dimensional conductor which goes beyond the usual linear response. In particular it includes Joule heating. We find that the nonlinear frequency-dependent conductivity is a constant. Surprisingly, the pressure remains isotropic. We also apply an electric field to a holographic insulator and show that there is a maximum electric field below which it can remain an insulator. Above this critical value, we argue that it becomes a conductor due to pair creation of charged particles. Finally, we study 1 + 1 and 3 + 1 dimensional conductors at the nonlinear level; here exact solutions are not available and a perturbative analysis shows that the current becomes time dependent, but in a way that is captured by a time-dependent effective temperature.

Physical Review Letters, 2008

We show that a simple gravitational theory can provide a holographically dual description of a superconductor. There is a critical temperature, below which a charged condensate forms via a second order phase transition and the (DC) conductivity becomes infinite. The frequency dependent conductivity develops a gap determined by the condensate. We find evidence that the condensate consists of pairs of quasiparticles.

Journal of High Energy Physics

We analytically compute the thermoelectric conductivities at zero frequency (DC) in the holographic dual of a four dimensional Einstein-Maxwell-Axion-Dilaton theory that admits a class of asymptotically hyperscaling violating Lifshitz backgrounds with a dynamical exponent z and hyperscaling violating parameter θ. We show that the heat current in the dual Lifshitz theory involves the energy flux, which is an irrelevant operator for z > 1. The linearized fluctuations relevant for computing the thermoelectric conductivities turn on a source for this irrelevant operator, leading to several novel and non-trivial aspects in the holographic renormalization procedure and the identification of the physical observables in the dual theory. Moreover, imposing Dirichlet or Neumann boundary conditions on the spatial components of one of the two Maxwell fields present leads to different thermoelectric conductivities. Dirichlet boundary conditions reproduce the thermoelectric DC conductivities obtained from the near horizon analysis of Donos and Gauntlett, while Neumann boundary conditions result in a new set of DC conductivities. We make preliminary analytical estimates for the temperature behavior of the thermoelectric matrix in appropriate regions of parameter space. In particular, at large temperatures we find that the only case which could lead to a linear resistivity ρ ∼ T corresponds to z = 4/3.

Journal of High Energy Physics

We investigate a massive gravity theory involving the SL(2, R) symmetry and anisotropy. Due to the SL(2, R) invariance of the equations of motion, the complex conductivity of this model transforms covariantly under the SL(2, R) transformation and the ratio of DC conductivities in different spatial directions is preserved even after the SL(2, R) transformation. We further investigate AC and Hall conductivities by utilizing the Kubo formula. There exists a Drude-like peak in the region with a small anisotropy, while such a Drude peak disappears when anisotropy becomes large. We also show that the complex conductivity can have a cyclotron frequency pole even beyond the hydrodynamic limit.

International Journal of Modern Physics A, 2012

The RG flow equation of various transport quantities are studied in arbitrary space–time dimensions, in the fixed as well as fluctuating background geometry both for the Maxwellian and DBI type of actions. The regularity condition on the flow equation of the conductivity at the horizon for the DBI action reproduces naturally the leading order result of Hartnoll et al. [J. High Energy Phys. 04, 120 (2010)]. Motivated by the result of van der Marel et al. [Science 425, 271 (2003], we studied, analytically, the conductivity versus frequency plane by dividing it into three distinct parts: ω < T, ω > T and ω ≫ T. In order to compare, we choose (3+1)-dimensional bulk space–time for the computation of the conductivity. In the ω < T range, the conductivity does not show up the Drude like form in any space–time dimensions. In the ω > T range and staying away from the horizon, for the DBI action with unit dynamical exponent, nonzero magnetic field and charge density, the conductiv...

Physical Review D, 2010

Recent work on holographic superconductivity and gravitational duals of systems with nonrelativistic 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 massive truncations is to only retain the lowest modes in the massive trajectories of the Kaluza-Klein mode decomposition of the original fields. This is an extension of the well-known result that consistent truncations may be obtained by restricting to the singlet sector of the internal symmetry group.

New Journal of Physics, 2011

Transitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semicircle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of the microscopic electrons. They would naturally follow if the low-energy transport properties were governed by an emergent discrete duality group relating the different plateaux, but no explicit examples of interacting systems having such a group are known. Recent progress using the AdS/CFT correspondence has identified examples with similar duality groups, but without the DC ohmic conductivity characteristic of quantum Hall experiments. We use this to propose a simple holographic model for low-energy quantum Hall systems, with a nonzero DC conductivity that automatically exhibits all of the observed consequences of duality, including the existence of the plateaux and the semicircle transitions between them. The model can be regarded as a strongly coupled analog of the old 'composite boson' picture of quantum Hall systems. Nonuniversal features of the model can be used to test whether it describes actual materials, and we comment on some of these in our proposed model.

Physical Review D

We study the deconfinement phase transition in (2 + 1)-dimensional holographic SU (N) gauge theories in the presence of an external magnetic field from the holographic hard and soft wall models. We obtain exact solutions for the critical temperature of the deconfinement transition for any range of magnetic field. As a consequence, we find a critical magnetic field (B c), in which the critical temperature (T c) vanishes; for B < B c we have an inverse magnetic catalysis and for B > B c we have a magnetic catalysis.

Physical Review D

We study the chiral symmetry breaking and restoration in (2 þ 1)-dimensional gauge theories from the holographic hardwall and softwall models. We describe the behavior of the chiral condensate in the presence of an external magnetic field for both models at finite temperature. For the hardwall model we find magnetic catalysis (MC) in different setups. For the softwall model we find inverse magnetic catalysis (IMC) and MC in different situations. We also find for the softwall model a crossover transition from IMC to MC at a pseudocritical magnetic field. This study also shows spontaneous symmetry breaking for both models. Interestingly, for B ¼ 0 in the softwall model, we found a nontrivial expectation value for the chiral condensate.

The European Physical Journal C

We study a holographic toy model by considering a probe fermion of finite charge density in an anisotropic background. By computing the fermionic spectral function numerically, we observed that the system exhibits some interesting behaviours in the nature of the Fermi surface (FS) and its evolution when tuning the controlling parameters. We introduced non-minimal interaction terms in the action for holographic fermions along with a complex scalar field but neglecting the backreaction of the fermions field on the background. Suppression in the spectral weight and deformation of FS is observed, which are reminiscent of the results seen in various condensed matter experiments in real materials.

Physical Review B, 2011

The pseudogap state of cuprate high-temperature superconductors has been often viewed as either a yet unknown competing order or a precursor state to superconductivity. While awaiting the resolution of the pseudogap problem in cuprates, we demonstrate that local pairing fluctuations, vortex liquid dynamics and other precursor phenomena can emerge quite generally whenever fermionic excitations remain gapped across the superconducting transition, regardless of the gap origin. Our choice of a tractable model is a lattice band insulator with short-range attractive interactions between fermions in the s-wave channel. An effective crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensate (BEC) regimes can be identified in any band insulator above two dimensions, while in two dimensions only the BEC regime exists. The superconducting transition is "unconventional" (non-pair-breaking) in the BEC regime, identified by either the bosonic mean-field or XY universality class. The insulator adjacent to the superconductor in the BEC regime is a bosonic Mott insulator of Cooper pairs, which may be susceptible to charge density wave ordering. We construct a function of the many-body excitation spectrum whose non-analytic changes define a sharp distinction between band and Mott insulators. The corresponding "second order transition" can be observed out of equilibrium by driving a Cooper pair laser in the Mott insulator. We explicitly show that the gap for charged bosonic excitations lies below the threshold for Cooper pair breakup in any BEC regime, despite quantum fluctuations. Our discussion ends with a view of possible consequences for cuprates, where antinodal pair dynamics has certain features in common with our simple s-wave picture.

Advances in Physics, 2011

An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature (strong-coupling)/high temperature (weak-coupling) dualities of classical statistical mechanics (or (Euclidean) path integrals). Its range of applications includes discrete lattice, continuum field, and gauge theories. Dualities are revealed to be local, structure-preserving mappings between model-specific bond algebras that can be implemented as unitary transformations, or partial isometries if gauge symmetries are involved. This characterization permits to search systematically for dualities and self-dualities in quantum models of arbitrary system size, dimensionality and complexity, and any classical model admitting a transfer matrix or operator representation. In particular, special dualities like exact dimensional reduction, emergent, and gauge-reducing dualities that solve gauge constraints can be easily understood in terms of mappings of bond algebras. As a new example, we show that the 2 Higgs model is dual to the extended toric code model in any number of dimensions. Non-local transformations like dual variables and Jordan-Wigner dictionaries are algorithmically derived from the local mappings of bond algebras. This permits to establish a precise connection between quantum dual and classical disorder variables. Our bond-algebraic approach goes beyond the standard approach to classical dualities, and could help resolve the long standing problem of obtaining duality transformations for lattice non-Abelian models. As an illustration, we present new dualities in any spatial dimension for the quantum Heisenberg model. Finally, we discuss various applications including location of phase boundaries, spectral behavior and, notably, we show how bond-algebraic dualities help constrain and realize fermionization in an arbitrary number of spatial dimensions.

Physical Review D, 2020

The carriers in graphene tuned close to the Dirac point envisage signatures of the strongly interacting fluid and are subject to hydrodynamic description. The important question is whether strong disorder induces the metal-insulator transition in this two-dimensional material. The bound on the conductivity tensor found earlier within the single current description, implies that the system does not feature metal-insulator transition. The linear spectrum of the graphene imposes the phase-space constraints and calls for the two-current description of interacting electron and hole liquids. Based on the gauge/gravity correspondence, using the linear response of the black brane with broken translation symmetry in Einstein-Maxwell gravity with the auxiliary U (1)-gauge field, responsible for the second current, we have calculated the lower bound of the DC-conductivity in holographic model of graphene. The calculations show that the bound on the conductivity depends on the coupling between both U (1) fields and for a physically justified range of parameters it departs only weakly from the value found for a model with the single U (1) field.

Physical Review D

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, chemical potentials both on the electric and magnetic side of the duality have to be introduced. A relation for the product of the nonabelian conductivities in the dual models is derived. We also conjecture a flavor S-duality transformation in the holographic dual to 3+1-dimensional QCD low-energy QCD with non-abelian flavor gauge groups. The conjectured S-duality interchanges isospin and baryonic chemical potentials.

Physical Review B, 2018

In the context of describing electrons in solids as a fluid in the hydrodynamic regime, we consider a flow of electrons in a channel of finite width, i.e. a Poiseuille flow. The electrons are accelerated by a constant electric field. We develop the appropriate relativistic hydrodynamic formalism in 2+1 dimensions and show that the fluid has a finite dc conductivity due to boundary-induced momentum relaxation, even in the absence of impurities. We use methods involving the AdS/CFT correspondence to examine the system in the strong-coupling regime. We calculate and study velocity profiles across the channel, from which we obtain the differential resistance dV /dI. We find that dV /dI decreases with increasing current I as expected for a Poiseuille flow, also at strong coupling and in the relativistic velocity regime. Moreover, we vary the coupling strength by varying η/s, the ratio of shear viscosity over entropy density. We find that dV /dI decreases when the coupling is increased. We also find that strongly coupled fluids are more likely to become ultra-relativistic and turbulent. These conclusions are insensitive to the presence of impurities. In particular, we predict that in channels which are clearly in the hydrodynamic regime already at small currents, the DC channel resistance strongly depends on η/s.

Modern Physics Letters A

In this paper, we review recent progress on relativistic hydrodynamics in (2 + 1) dimensions with an external magnetic field. We discuss the formalism allowing for momentum loss due to the explicit and spontaneous breaking of translation invariance by scalar operators. We also compare to some results from the gauge/gravity correspondence.

Physical Review D, 2010

We study a charged dilatonic black hole in AdS 5 , derived from a lagrangian involving a gauge field whose kinetic term is modified by the exponential of a neutral scalar. This black hole has two properties which one might reasonably demand of the dual of a Fermi liquid: Its entropy is proportional to temperature at low temperature, and its extremal limit supports normal modes of massless, charged bulk fermions. The black hole we study has a simple analytic form because it can be embedded in type IIB string theory as the nearhorizon limit of D3-branes with equal spins in two of the three independent transverse planes. Two further properties can be deduced from this embedding: There is a thermodynamic instability, reminiscent of ferromagnetism, at low temperatures; and there is an AdS 3 factor in the extremal near-horizon geometry which accounts for the linear dependence of entropy on temperature. Altogether, it is plausible that the dilatonic black hole we study, or a relative of it with similar behavior in the infrared, is the dual of a Fermi liquid; however, the particular embedding in string theory that we consider is unlikely to have such a dual description, unless through some unexpected boson-fermion equivalence at large N .

Physical Review Letters, 2009

We consider zero temperature solutions to the Abelian Higgs model coupled to gravity with a negative cosmological constant. With appropriate choices of parameters, the geometry contains two copies of anti-de Sitter space, one describing conformal invariance in the ultraviolet, and one in the infrared. The effective speed of signal propagation is smaller in the infrared. Green's functions and associated transport coefficients can have unusual power law scaling in the infrared. We provide an example in which the real part of the conductivity scales approximately as ω 3.5 for small ω.

Journal of High Energy Physics

We study nonlinear energy diffusion in the SYK chain within the framework of Schwinger-Keldysh effective field theory. We analytically construct the corresponding effective action up to 40th order in the derivative expansion. According to this effective action, we calculate the first order loop correction of the energy density response function, whose pole is the dispersion relation of energy diffusion. As expected, the standard derivative expansion of the classical dispersion relation breaks down due to the long-time tails. However, we find that the nonlinear contributions are so that one can still derive the dispersion relation in the power series. In fact, due to the long-time tails, the classical dispersion relation is split into two series distinct from the derivative expansion, and we show they are convergent. The radius of convergence is proportional to the ratio of thermal conductivity to diffusion constant.

Journal of High Energy Physics, 2008

We study the charge transport properties of fields confined to a (2+1)-dimensional defect coupled to (3+1)-dimensional super-Yang-Mills at large-N c and strong coupling, using AdS/CFT techniques applied to linear response theory. The dual system is described by N f probe D5-or D7-branes in the gravitational background of N c black D3-branes. Surprisingly, the transport properties of both defect CFT's are essentially identical-even though the D7-brane construction breaks all supersymmetries. We find that the system possesses a conduction threshold given by the wave-number of the perturbation and that the charge transport arises from a quasiparticle spectrum which is consistent with an intuitive picture where the defect acquires a finite width. We also examine finite-λ modifications arising from higher derivative interactions in the probe brane action.

Physical review, 2010

The holographic model for S-wave high T c superconductors developed by Hartnoll, Herzog and Horowitz is generalised to describe D-wave superconductors. The 3+1 dimensional gravitational theory consists of a symmetric, traceless second-rank tensor field and a U (1) gauge field in the background of the AdS black hole. Below T c the tensor field which carries the U (1) charge undergoes the Higgs mechanism and breaks the U (1) symmetry of the boundary theory spontaneously. The phase transition characterised by the D-wave condensate is second order with the mean field critical exponent β = 1/2. As expected, the AC conductivity is isotropic below T c and the system becomes superconducting in the DC limit but has no hard gap.

Physical review, 2010

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-Tc superconductors. We also find a linear relation between the gap in the fermionic spectrum and the condensate, indicating the condensate is formed by fermion pairing.

Journal of High Energy Physics, 2017

We examine Penrose limits of the duality proposed by Guarino, Jafferis and Varela between a type IIA massive background of the type of a warped, squashed AdS 4 ×S 6 , and a 2+1 dimensional IR fixed point of N = 8 super Yang-Mills deformed by Chern-Simons terms to N = 2 supersymmetry. One type of Penrose limit for closed strings corresponds to a large charge closed spin chain, and another, for open strings on giant graviton D-branes, corresponds to an open spin chain on sub-determinant operators. For the first limit, we find that like in the ABJM case, there are functions f a (λ) that interpolate between the perturbative and nonperturbative (string) regions for the magnon energy. For the second, we are unable to match the gravity result with the expected field theory result, making this model more interesting than ones with more supersymmetry.

Physics Letters B, 2022

Holographic properties of a finite density fermion system have been shown to exhibit many interesting behaviours which can be observed in future. In this paper, we study low energy fermion properties in the framework of holographic Mott-Insulator system. We study the nature of the Fermi surface and its evolution by tuning both Lorentz preserving and violating dipole coupling in the bulk. We further introduce translational symmetry breaking complex scalar field, which is assumed to couple with the holographic fermions. The symmetry breaking background induced by the scalar field is known as Qlattice. We calculate the fermion spectral function which captures the low energy behaviour of the system. By tuning the dipole parameters as well as the non-normalizable component of the scalar field, we observe interesting phenomena such as spectral weight transfer, Fermi surface smearing, which has already been reported in various real condensed matter experiments.

Journal of High Energy Physics, 2021

We analyse near-extremal black brane configurations in asymptotically AdS4 spacetime with the temperature T, chemical potential μ, and three-velocity uν, varying slowly. We consider a low-temperature limit where the rate of variation is much slower than μ, but much bigger than T. This limit is different from the one considered for conventional fluid-mechanics in which the rate of variation is much smaller than both T, μ. We find that in our limit, as well, the Einstein-Maxwell equations can be solved in a systematic perturbative expansion. At first order, in the rate of variation, the resulting constitutive relations for the stress tensor and charge current are local in the boundary theory and can be easily calculated. At higher orders, we show that these relations become non-local in time but the perturbative expansion is still valid. We find that there are four linearised modes in this limit; these are similar to the hydrodynamic modes found in conventional fluid mechanics with th...

Physical Review D, 2010

We investigate properties of holographic strange metals in p + 2-dimensions, generalizing the analysis performed in arXiv:0912.1061. The bulk spacetime is p + 2-dimensional Lifshitz black hole, while the role of charge carriers is played by probe D-branes. We mainly focus on massless charge carriers, where most of the results can be obtained analytically. We obtain exact results for the free energy and calculate the entropy density, the heat capacity as well as the speed of sound at low temperature. We obtain the DC conductivity and DC Hall conductivity and find that the DC conductivity takes a universal form in the large density limit, while the Hall conductivity is also universal in all dimensions. We also study the resistivity in different limits and clarify the condition for the linear dependence on the temperature, which is a key feature of strange metals. We show that our results for the DC conductivity are consistent with those obtained via Kubo formula and we obtain the charge diffusion constant analytically. The corresponding properties of massive charge carriers are also discussed in brief.