We explore the state of matter characterized by the charged timelike vector order parameter. We employ holographic duality in order to construct such a state and study its thermoelectric transport, fermionic spectral function and the character of the Meissner effect. We uncover the unusual features of this “timelike superconductor”: the absence of the gap in the fermionic spectrum and co-existence of Drude peak and supercurrent in the AC transport, which are reminiscent to those of time-reversal-odd and gapless superconductors, correspondingly. We show that this state is dynamically stable and thermodynamically at least metastable. Along the way we develop the holographic model of the charged vector field, which acquires mass due to a variant of the Stueckelberg mechanism with the adjoint Higgs field.

The anomalous strange metal phase found in high-Tc cuprates does not follow the conventional condensed-matter principles enshrined in the Fermi liquid and presents a great challenge for theory. Highly precise experimental determination of the electronic self-energy can provide a test bed for theoretical models of strange metals, and angle-resolved photoemission can provide this as a function of frequency, momentum, temperature and doping. Here we show that constant energy cuts through the nodal spectral function in (Pb,Bi)2Sr2−xLaxCuO6+δ have a non-Lorentzian lineshape, consistent with a self-energy that is k dependent. This provides a new test for aspiring theories. Here we show that the experimental data are captured remarkably well by a power law with a k-dependent scaling exponent smoothly evolving with doping, a description that emerges naturally from anti-de Sitter/conformal-field-theory based semi-holography. This puts a spotlight on holographic methods for the quantitative modelling of strongly interacting quantum materials like the cuprate strange metals.

We demonstrate that the absence of stable quasiparticle excitations on parts of the Fermi surface, similar to the "nodal-antinodal dichotomy" in underdoped cuprate su-perconductors, can be reproduced in models of strongly correlated electrons defined via a holographic dual. We show analytically that the anisotropy of the quantum critical continuum, which is a feature of these models, may lead to washing out the quasipar-ticle peak in one direction while leaving it intact in the perpendicular one. The effect relies on the qualitatively different scaling of the self-energy in different directions. Us-ing the explicit example of the anisotropic Q-lattice model, we demonstrate how this effect emerges due to specific features of the near horizon geometry of the black hole in the dual description.

Quantum strongly correlated matter exhibits properties which are not easily explainable in the conventional framework of Fermi liquids. Universal effective field theory tools are applicable in these cases regardless of the microscopic details of the quantum system, since they are based on symmetries. It is necessary, however, to construct these effective tools in full generality, avoiding restrictions coming from particular microscopic descriptions which may inadequately constrain the coefficients that enter in the effective theory. In this work we demonstrate with explicit examples how the hydrodynamic coefficients, which have been recently reinstated in the effective theory of pinned charge density waves (CDWs), can affect the phenomenology of the thermoelectric transport in strongly correlated quantum matter. Our examples, based on two classes of holographic models with pinned CDW, have microscopics which are conceptually different from Fermi liquids. Therefore, the above transport coefficients are nonzero, contrary to the conventional approach. We show how these coefficients allow one to take into account the change of sign of the Seebeck coefficient and the low resistivity of the CDW phase of the cuprate high temperature superconductors, without referring to the effects of Fermi surface reconstruction.

We study the dynamics of spontaneous translation symmetry breaking in holographic models in presence of weak explicit sources. We show that, unlike conventional gapped quantum charge density wave systems, this dynamics is well characterized by the effective time dependent Ginzburg-Landau equation, both above and below the critical temperature, which leads to a "gapless" algebraic pattern of metal-insulator phase transition. In this framework we elucidate the nature of the damped Goldstone mode (the phason), which has earlier been identified in the effective hydrodynamic theory of pinned charge density wave and observed in holographic homogeneous lattice models. We follow the motion of the quasinormal modes across the dynamical phase transition in models with either periodic inhomogeneous or helical homogeneous spatial structures, showing that the phase relaxation rate is continuous at the critical temperature. Moreover, we find that the qualitative low-energy dynamics of the broken phase is universal, insensitive to the precise pattern of translation symmetry breaking, and therefore applies to homogeneous models as well.

An interesting application of the gauge/gravity duality to condensed matter physics is the description of a lattice via breaking translational invariance on the gravity side. By making use of global symmetries, it is possible to do so without scarifying homogeneity of the pertinent bulk solutions, which we thus term as "homogeneous holographic lattices." Due to their technical simplicity, these configurations have received a great deal of attention in the last few years and have been shown to correctly describe momentum relaxation and hence (finite) DC conductivities. However, it is not clear whether they are able to capture other lattice effects which are of interest in condensed matter. In this paper we investigate this question focusing our attention on the phenomenon of commensurability, which arises when the lattice scale is tuned to be equal to (an integer multiple of) another momentum scale in the system. We do so by studying the formation of spatially modulated phases in various models of homogeneous holographic lattices. Our results indicate that the onset of the instability is controlled by the near horizon geometry, which for insulating solutions does carry information about the lattice. However, we observe no sharp connection between the characteristic momentum of the broken phase and the lattice pitch, which calls into question the applicability of these models to the physics of commensurability.

We study the relationship between chiral symmetry breaking and baryons in holographic QCD. We construct a soliton with unit baryon charge in the presence of a nonzero mean value of the scalar bifundamental field, which is dual to the chiral condensate. We obtain a relation between the chiral condensate and the mass of the baryon and find in a clear-cut way that at large values of the condensate the holographic soliton is no longer located on the IR wall. Instead it is split into two halves, which are symmetrically located on the left and right flavor branes. On the other hand we find that the local value of the quark condensate is suppressed in the core of the soliton, which is evidence for a partial chiral symmetry restoration inside the baryon.

We study local temperature fluctuations in a 2+1 dimensional CFT on the sphere, dual to a black hole in asymptotically AdS spacetime. The fluctuation spectrum is governed by the lowest-lying hydrodynamic modes of the system whose frequency and damping rate determine whether temperature fluctuations are thermal or quantum. We calculate numerically the corresponding quasinormal frequencies and match the result with the hydrodynamics of the dual CFT at high temperature. As a by-product of our analysis we determine the appropriate boundary conditions for calculating low-lying quasinormal modes for a four-dimensional Reissner-Nordstrom black hole in global AdS.

We study different phases in the holographic model of d-wave superconductor. These are described by solutions to the classical equations of motion found in different ansatze. Apart from the known homogeneous d-wave superconducting phase we find three new solutions. Two of them represent two distinct families of the spatially modulated solutions, which realize the charge density wave phases in the dual theory. The third one is the new homogeneous phase with nonzero anapole moment. These phases are relevant to the physics of cuprate high-Tc superconductor in pseudogap region. While the d-wave phase preserves translation, parity and time reversal symmetry, the striped phases break translations spontaneously. Parity and time-reversal are preserved when combined with discrete half-periodic shift of the wave. In anapole phase translation symmetry is preserved, but parity and time reversal are spontaneously broken. All of the considered solutions break the global U(1). Thermodynamical treatment shows that in the simplest d-wave model the anapole phase is always preferred, while the stripe phases realize the continuous transition in solution space between the normal phase and two homogeneous condensed phases.

We briefly review the generalized Skyrmion model for the baryon recently suggested by us. It takes into account the tower of vector and axial mesons as well as the chiral symmetry breaking. The generalized Skyrmion model provides the qualitative explanation of the Ioffe's formula for the baryon mass.