Several classes of gravitational backgrounds in $3+1$ dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in $2+1$ dimensions with critical exponent $z\geq 1$. We numerically explore one such model, characterized by a temperature $T$ and chemical potential $μ$, and find how to embed these solutions into AdS for a range of values of $z$. We find no phase transition going from the $T\llμ$ to the $T\gg μ$ regimes, and find that the solutions smoothly interpolate between the Lifshitz-like behavior and the relativistic AdS-like behavior. Finally, we exploit some conserved quantities to find a relationship between the energy density $\mc E$, entropy density $s$, and number density $n$, $\mc E=\frac{2}{3} \left(Ts+μn\right)$. We show that this result is expected from general scaling arguments, and generalizes to $\mc E= \frac{d}{d+1}\left(Ts+μn\right)$ for a theory dual to AdS$_{d+2}$ (Poincaré patch) asymptotics with a local $U(1)$ gauge invariance.
We study quasi-normal modes for a higher dimensional black hole with Lifshitz scaling, as these quasi-normal modes can be used to test Lifshitz models with large extra dimensions. Furthermore, as the effective Planck scale is brought down in many models with large extra dimensions, we study these quasi-normal modes for a UV completion action. Thus, we analyze quasi-normal modes for higher dimensional dilaton-Lifshitz black hole solutions coupled to a non-linear Born-Infeld action. We will analyze the charged perturbations for such a black hole solution. We will first analyze the general condit…
We study electromagnetically charged dilatonic black brane solutions in arbitrary dimensions with flat transverse spaces, that are asymptotically AdS. This class of solutions includes spacetimes which possess a bulk region where the metric is approximately invariant under Lifshitz scalings. Given fixed asymptotic boundary conditions, we analyze how the behavior of the bulk up to the horizon varies with the charges and derive the extremality conditions for these spacetimes.
We construct analytic solutions describing black holes and black branes in asymptotically Lifshitz spacetimes with arbitrary dynamical exponent z and for arbitrary number of dimensions. The model considered consists of Einstein gravity with negative cosmological constant, a scalar, and N U(1) gauge fields with dilatonic-like couplings. We study the phase diagrams and thermodynamic instabilities of the solution, and find qualitative differences between the cases with 1<= z<2, z=2 and z>2.
In this paper we have considered the structure of the non-projectable Horava-Melby-Thompson (HMT) gravity to find braneworld scenarios. A relativistic scalar field is considered in the matter sector and we have shown how to reduce the equations of motion to first-order differential equations. In particular, we have studied thick brane solutions of both the dilatonic and Randall-Sundrum types.
We construct Lifshitz-like Janus solutions in the Einstein-scalar theory with cosmological constant in arbitrary dimensions. They are holographically dual to z=2 Lifshitz-like field theories with a defect. The four-dimensional solutions can be embedded into type IIB supergravity as dilatonic deformations of AdS_5 x Y^5 with three-form field strengths, where Y^5 is a five-dimensional Einstein manifold.
We study Einstein-Maxwell-dilaton gravity models in four-dimensional anti-de Sitter (AdS) spacetime which admit the Reissner-Nordstrom (RN) black hole solution. We show that below a critical temperature the AdS-RN solution becomes unstable against scalar perturbations and the gravitational system undergoes a phase transition. We show using numerical calculations that the new phase is a charged dilatonic black hole. Using the AdS/CFT correspondence we discuss the phase transition in the dual field theory both for non-vanishing temperatures and in the extremal limit. The extremal solution has a …
We construct and study general static, spherically symmetric, magnetically charged solutions in Einstein-Maxwell-dilaton gravity in four dimensions. That is, taking Einstein gravity coupled to a ${\rm U}(1)$ gauge field and a massless dilaton$\unicode{x2014}$e.g., the action in the low-energy limit of string theory or Kaluza-Klein reduction$\unicode{x2014}$with arbitrary dilaton coupling, we build a three-parameter family of objects characterized by their mass, charge, and dilaton flux, generalizing the well known Garfinkle-Horowitz-Strominger black hole. We analyze the near-extremal and near-…
In this work, we study the existence of asymptotically Lifshitz black holes in Critical Gravity in four dimensions with a negative cosmological constant under two scenarios: First, including dilatonic fields as the matter source, where we find an asymptotically Lifshitz solution for a fixed value of the dynamical exponent $z=4$. As a second case, we also added a non-minimally coupled scalar field $Φ$ with a potential given by a mass term and a quartic term. Using this approach, we found a solution for $z$ defined in the interval $(1,4)$, recovering the Schwarzchild-Anti-de Sitter case with pla…
We consider charged dilatonic black branes in AdS_5 and examine the effects of perturbative higher derivative corrections on the ratio of shear viscosity to entropy density eta/s of the dual plasma. The structure of eta/s is controlled by the relative hierarchy between the two scales in the plasma, the temperature and the chemical potential. In this model the background near-horizon geometry interpolates between a Lifshitz-like brane at low temperature, and an AdS brane at high temperatures -- with AdS asymptotics in both cases. As a result, in this construction the viscosity to entropy ratio …
By imposing the relativistic boundary term and Lorentz violating that in the dilatonic black brane with a Lifshitz like IR geometry and $AdS_4$ boundary, we study the properties of the spectral functions of the fermions. We find that in the two fixed points, there are emergent Fermi-surface structures and many properties seem to be in agreement with that of Fermi liquid. Especially, the low energy behavior exhibits a linear dispersion relation. In addition, we also find that a holographic flat band also emerges in this background of the dilatonic black brane.
Recently proposed Horava-Lifshitz gravity promises a UV completion of Einstein's theory by sacrificing general covariance at short distances and introducing anisotropic spacetime scaling. Here we present a dyonic solution by coupling this theory to a vector field and we discuss some properties of solution.
We obtain the Lifshitz UV completion in a specific model for z=2 Lifshitz geometries. We use a vielbein formalism which enables identification of all the sources as leading components of well-chosen bulk fields. We show that the geometry induced from the bulk onto the boundary is a novel extension of Newton-Cartan geometry with a specific torsion tensor. We explicitly compute all the vevs including the boundary stress-energy tensor and their Ward identities. After using local symmetries/Ward identities the system exhibits 6+6 sources and vevs. The FG expansion exhibits, however, an additional …
We consider a gravitational theory with two Maxwell fields, a dilatonic scalar and spatially dependent axions. Black brane solutions to this theory are Lifshitz-like and violate hyperscaling. Working with electrically charged solutions, we calculate analytically the holographic DC conductivities when both gauge fields are allowed to fluctuate. We discuss some of the subtleties associated with relating the horizon to the boundary data, focusing on the role of Lifshitz asymptotics and the presence of multiple gauge fields. The axionic scalars lead to momentum dissipation in the dual holographic …
We construct a Lifshitz-like version of five-dimensional (5D) QED which is UV - completed and reduces at low energies to ordinary 5D QED. The UV quantum behaviour of this theory is very smooth. In particular, the gauge coupling constant is finite at all energy scales and at all orders in perturbation theory. We study the IR properties of this theory, when compactified on a circle, and compare the one-loop energy dependence of the coupling in the Lifshitz theory with that coming from the standard 5D QED effective field theory. The range of validity of the 5D effective field theory is found to a…
We consider asymptotically-AdS $n$-dimensional black brane solutions in a theory of gravity coupled to a set of $N$ $p$-form field strengths, in which the field strengths carry magnetic charges. For appropriately chosen charges, the metrics are isotropic in the $(n-2)$ transverse directions. However, in general the field strength configurations break the full Euclidean symmetry of the $(n-2)$-dimensional transverse space. We then study the linearised equation for transverse traceless metric perturbations in these backgrounds, and by employing the Kubo formula we obtain expressions for $η/S$, t…
We study solutions to Einstein-Maxwell-dilaton gravity with a constant magnetic flux which describe, in the holographic AdS/CFT framework, field theories characterized by a dynamical critical exponent and a hyperscaling violation exponent. Such solutions are known to be IR-incomplete due to the presence of a running dilaton, which drives the theory towards strong coupling in the IR, where quantum corrections become important. After introducing generic corrections, in this note we examine the conditions for the emergence of an AdS_2 x R^2 region close to the horizon, which provides an IR-comple…
We construct Lifshitz scalar field theories in 4+1 dimensions which retain 3+1-d Lorentz invariance and therefore ensure a unique limiting speed in the 3+1-d world. Such a construction is potentially useful in developing field-theoretic ultraviolet completions of extra-dimensional field theories. The extra dimension y is treated asymmetrically from the usual three spatial dimensions by introducing derivatives of order 2n with respect to y in the action. We show that lambda phi^4 theory becomes progressively less non-renormalisable by power counting as n is increased. This suggests that the non…
We show that the Horava theory for the completion of General Relativity at UV scales can be interpreted as a gauge fixed theory, and it can be extended to an invariant theory under the full group of four-dimensional diffeomorphisms. In this respect, although being fully relativistic, it results to be locally anisotropic in the time-like and space-like directions defined by a family of irrotational observers. We show that this theory propagates generically three degrees of freedom: two of them are related to the four-dimensional diffeomorphism invariant graviton (the metric) and one is related …
We study a five dimensional Horava-Lifshitz like scalar QED with dynamical exponent z=2. Consistency of the renormalization procedure requires the presence of four quartic and one six-fold scalar couplings besides the terms bilinear in the scalar fields. We compute one-loop radiative corrections to the parameters in the original Lagrangian employing dimensional regularization in the spacial part of the Feynman integrals and prove the relevant Ward identities. By using renormalization group methods, we determine the behavior of the coupling constants with changes in the energy and discuss the e…
We present a candidate quantum field theory of gravity with dynamical critical exponent equal to z=3 in the UV. (As in condensed matter systems, z measures the degree of anisotropy between space and time.) This theory, which at short distances describes interacting nonrelativistic gravitons, is power-counting renormalizable in 3+1 dimensions. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory flows naturally to the relativistic…
In five dimensions, we consider a model described by the Einstein gravity with a source given by a scalar field and various Abelian gauge fields with dilatonic-like couplings. For this model, we are able to construct two dyonic black holes whose three-dimensional horizons are modeled by two nontrivial homogeneous Thurston's geometries. The dyonic solutions are of Lifshitz type with an arbitrary value of the dynamical exponent. In fact, the first gauge field ensures the anisotropy asymptotic while the remaining Abelian fields sustain the electric and magnetic charges. Using the Hamiltonian form…
