We consider $CP^{N-1}$ models in $d+1$ dimensions around Lifshitz fixed points with dynamical critical exponent $z$, in the large-N expansion. It is shown that these models are asymptotically free and dynamically generate a mass for the $CP^{N-1}$ fields for all $d=z$. We demonstrate that, for $z=d=2$, the initially nondynamical gauge field acquires kinetic terms in a way similar to usual $CP^{N-1}$ models in 1+1 dimensions. Lorentz invariance emerges generically in the low-energy electrodynamics, with a nontrivial dielectric constant given by the inverse mass gap and a magnetic permeability which has a logarithmic dependence on scale. At a special multicritical point, the low-energy electrodynamics also has $z=2$, and an essentially singular dependence of the effective action on $B=ε_{ij}\partial_iA_j$.
We analytically describe the properties of the s-wave holographic superconductor with the Exponential nonlinear electrodynamics in the Lifshitz black hole background in four-dimensions. Employing an assumption the scalar and gauge fields backreact on the background geometry, we calculate the critical temperature as well as the condensation operator. Based on Sturm-Liouville method, we show that the critical temperature decreases with increasing exponential nonlinear electrodynamics and Lifshitz dynamical exponent, z, indicating that condensation becomes difficult. Also we find that the effects…
In this work the generation of generalized Chern-Simons terms in three dimensional quantum electrodynamics with high spatial derivatives is studied. We analyze the self-energy corrections to the gauge field propagator by considering an expansion of the amplitude up to third order in the external momenta. The divergences of the corrections are determined and explicit forms for the Chern-Simons terms with high derivatives are obtained. Some unusual aspects of the calculation are stressed and the existence of a smooth isotropic limit is proved. The transversality of the anisotropic gauge propagat…
In this work, we consider the Hořava-Lifshitz scaling to rewrite higher-order derivatives in Lorentz-violating CPT-even electrodynamics. The possibility of the Lorentz invariance violation being originally suppressed by the quantum gravity energy scale $M_{\rm QG}$, may be indeed circumvented in a scenario with anisotropy between space and time above certain intermediate energy scale $Λ_{\rm HL} \ll M_{\rm QG}$. To test the model, we have used observational results of a cosmological time delay between high and low energy photons from gamma ray bursts (GRB090510) event. For specific values of t…
In this paper, we construct a new class of topological black hole Lifshitz solutions in the presence of nonlinear exponential electrodynamics for Einstein-dilaton gravity. We show that the reality of Lifshitz supporting Maxwell matter fields exclude the negative horizon curvature solutions except for the asymptotic AdS case. Calculating the conserved and thermodynamical quantities, we obtain a Smarr type formula for the mass and confirm that thermodynamics first law is satisfied on the black hole horizon. Afterward, we study the thermal stability of our solutions and figure out the effects of …
We employ gauge/gravity duality to study the effects of Lifshitz scaling on the holographic $p$ wave superconductors in the presence of Born-Infeld (BI) nonlinear electrodynamics. By using the shooting method in the probe limit, we calculate the relation between critical temperature $T_{c}$ and $ρ^{z/d}$ numerically for different values of mass, nonlinear parameter $b$ and Lifshitz critical exponent $z$ in various dimensions. We observe that critical temperature decreases by increasing $b$, $z$ or the mass parameter $m$ which makes conductor/superconductor phase transition harder to form. In a…
Charged Lifshitz black holes for the Einstein-Proca-Maxwell system with a negative cosmological constant in arbitrary dimension $D$ are known only if the dynamical critical exponent is fixed as $z=2(D-2)$. In the present work, we show that these configurations can be extended to much more general charged black holes which in addition exist for any value of the dynamical exponent $z>1$ by considering a nonlinear electrodynamics instead of the Maxwell theory. More precisely, we introduce a two-parametric nonlinear electrodynamics defined in the more general, but less known, so-called $(\mathcal{…
Mainly on nano-scale, but maybe not exclusively, it can be imagined a spontaneous charge disjunction inside certain media due to the fluctuations, collisions, wall effects, radiation or/and other presently unknown interactions. The repulsive Casimir-Lifshitz force may be also a good candidate as a source of this kind of phenomenon. To cover this assumption mathematically an additional term should appear in the Maxwell equations. As a consequence of this term, similar Klein-Gordon equations with a negative mass term will be obtained for the electric and magnetic fields. These equations may have…
Using the Dirac Method, we study the Hamiltonian consistency for three field theories. First we study the electrodynamics a la Hořava and we show that this system is consistent for an arbitrary dynamical exponent $z.$ Second, we study a Lifshitz type electrodynamics, which was proposed in [1]. For this last system we found that the canonical momentum and the electrical field are related through a Proca type Green function, however this system is consistent. In addition, we show that the anisotropic Yang-Mills theory with dynamical exponent $z=2$ is consistent. Finally, we study a generalized a…
In this paper, we first obtain the ($n+1$)-dimensional dilaton-Lifshitz black hole (BH) solutions in the presence of Born-Infeld (BI) electrodynamics. We find that there are two different solutions for $z=n+1$ and $z\neq n+1$ cases ($z$ is dynamical critical exponent). We show that the thermodynamics first law is satisfied for both cases. Then, we turn to study different phase transitions (PTs) for our BHs. We start with study of Hawking-Page PT for both linearly and BI charged BHs. After that, we discuss the PTs inside the BHs. We present the improved Davies quantities and prove that the PT p…
We discuss in this paper the vacuum Cherenkov radiation in the $z=2$ Lifshitz electrodynamics. The improved ultraviolet behavior, in terms of higher spatial derivatives, and the renormalizable couplings, due to the time-space anisotropic scaling, present in the Lifshitz setting are extremely important in fulfilling the physical constraints in order to this vacuum process to happen. We evaluate in details the instantaneous rate of energy loss for a charge, and also analyze the emission of very soft photons in this framework.
Effective Lifshitz-Born-Infeld black holes from general covariance breaking
Universidade Estadual da Paraíba（帕拉伊巴州立大学）；Universidade Federal Rural do Semi-Árido（半干旱地区联邦农村大学）；Universidade Federal da Campina Grande（大坎皮纳联邦大学）；Universidade Federal de Campina Grande（大坎皮纳联邦大学）
We consider 2+1 dimensional compact U(1) gauge theory at the Lifshitz point with dynamical critical exponent $z=2$. As in the usual $z=1$ theory, monopoles proliferate the vacuum for any value of the coupling, generating a mass scale. The theory of the dilute monopole gas is written in terms a non-relativistic Sine-Gordon model with two real fields. While monopoles remove some of the massless poles of the perturbative field strength propagator, a gapless mode representing the incomplete screening of monopoles remains, and is protected by a shift invariance of the original theory. Timelike Wils…
The quantum Lifshitz model provides an effective description of a quantum critical point. It has been shown that even though non--Lorentz invariant, the action admits a natural supersymmetrization. In this note we introduce a perturbative framework and show how the supersymmetric structure can be used to greatly simplify the Feynman rules and thus the study of the model.
We construct supersymmetric Lifshitz field theories with four real supercharges in a general number of space dimensions. The theories consist of complex bosons and fermions and exhibit a holomorphic structure and non-renormalization properties of the superpotential. We study the theories in a diverse number of space dimensions and for various choices of marginal interactions. We show that there are lines of quantum critical points with an exact Lifshitz scale invariance and a dynamical critical exponent that depends on the coupling constants.
In this paper, using the techniques of Gauge/gravity duality we explore the hydrodynamic regime of $ z=3 $ Lifshitz fixed points in $ 1+1 $ dimensions. The speed of sound in the non-relativistic plasma turns out to be $\sqrt{3}$, which clearly violates the conjectured upper bound. We identify this as a natural consequence of the Lorentz symmetry breakdown at $ z=3 $ Lifshitz fixed point. In our analysis, we compute bulk viscosity to entropy ratio for quantum field theory dual to Lifshitz gravity in $ 2+1$ dimensions and it turns out that for this particular holographic model this ratio is abov…
We propose a model with quantum bosons on the fcc lattice, which has a stable algebraic Bose liquid phase at low energy. We show that this phase is described by emergent quantum gravity at the Gaussian z = 3 Lifshitz fixed point in 3+1 dimensions. The stability of this algebraic Bose liquid phase is guaranteed by the gauge symmetry of gravitons and self-duality of the low energy field theory. By tuning one parameter in the lattice boson model we can drive a phase transition between the z = 3 Lifshitz gravity and another algebraic Bose liquid phase, described by gravity at the z = 2 Lifshitz po…
We disclose the effects of Lifshitz dynamical exponent $z$ on the properties of holographic paramagnetic-ferromagnetic phase transition in the background of Lifshitz spacetime. To preserve the conformal invariance in higher dimensions, we consider the Power-Maxwell (PM) electrodynamics as our gauge field. We introduce a massive $2$-form coupled to the PM field and perform the numerical shooting method in the probe limit by assuming the PM and the $2$-form fields do not back-react on the background geometry. The obtained results indicate that the critical temperature decreases with increasing t…
We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent $z$, which governs the anisotropy between spatial and temporal scaling $t \to λ^z t$, $x \to λx$; we focus on the case with $z=2$. Such theories describe multicritical points in certain m…
Lifshitz critical points meet Zamolodchikov perturbation theory
Laboratoire de Physique de l’École Normale Supérieure, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，巴黎文理研究大学，法国国家科学研究中心，索邦大学，巴黎西岱大学）
We consider the gravity dual of strongly coupled system at a Lifshitz-fixed point and finite temperature, which was constructed in a recent work arXiv:0909.0263. We construct an Abelian Higgs model in that background and calculate condensation and conductivity using holographic techniques. We find that condensation happens and DC conductivity blows up when temperature turns below a critical value.
We construct the general O(N)-symmetric non-linear sigma model in 2+1 spacetime dimensions at the Lifshitz point with dynamical critical exponent z=2. For a particular choice of the free parameters, the model is asymptotically free with the beta function coinciding to the one for the conventional sigma model in 1+1 dimensions. In this case, the model admits also a simple description in terms of adjoint currents.
I discuss the von Neumann entanglement entropy in two-dimensional quantum Lifshitz criical point, namely in Rokhsar-Kivelson type critical wavefunctions. I follow the approach proposed by B. Hsu et al. [Phys. Rev. B 79, 115421 (2009)], but point out a subtle problem concerning compactification of replica boson fields: although one can define a set of new boson fields by linear combinations of the original fields, the new fields are not compactified independently. In order to systematically study boundary conformal field theory of multicomponent free bosons, I employ a geometric formulation bas…
The presence of isotropic Lifshitz points for a U(1) symmetric scalar theory is investigated with the help of the Functional Renormalization Group at the conjectured lower critical dimension d=4. To this aim, a suitable truncation in the expansion of the effective action in powers of the field is considered and, consequently, the Renormalization Group flow is reduced to a set of ordinary differential equations for the parameters that define the effective action. Within this approximation, indications of a line of Lifshitz points are found, that present evident similarities with the properties …
An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the $O(ε^{2}) $ calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations $O(ε) $ finally uns…
We give a new twist to an old-fashioned topic in quantum field theory describing violations of the chiral charge conservation of massless fermions through Adler-Bell-Jackiw anomalies in the background of instanton fields in the context of non-relativistic Lifshitz theories. The results we report here summarize in a nut-shell our earlier work on the subject found in arXiv:1103.5693 and arXiv:1110.1332. We present simple examples where index computations can be carried out explicitly focusing, in particular, to gravitational models of Lifshitz type and highlight their differences from ordinary g…
We describe new universality classes associated to generic higher character Lifshitz critical behaviors for systems with arbitrary short range competing interactions. New renormalization-group arguments are proposed for anisotropic and isotropic systems. The usual $m$-axial Lifshitz universality classes are obtained as a simple limit of this arbitrary competing critical behavior.
We solve a renormalized Wheeler-DeWitt equation for Einstein gravity in D+1 dimensions with D= odd in the strong coupling limit, which is expected to be suited to probe quantum geometry at short distances, in order to test Horava's idea that quantum gravity at short distances will be described by a nonrelativistic system with dynamical critical exponent z>1. Our results support the idea and show that the Wheeler-DeWitt equation possesses a solution associated with a z=2 Lifshitz point but no other z>2 solutions to leading order of the strong coupling expansion.
The presence of isotropic Lifshitz points for a O(N)-symmetric scalar theory is investigated with the help of the Functional Renormalization Group. In particular, at the supposed lower critical dimension d=4, evidence for a continuous line of fixed points is found for the O(2) theory, and the observed structure presents clear similarities with the properties observed in the 2-dimensional Berezinskii-Kosterlitz-Thouless phase.
The susceptibility amplitude ratio in the neighborhood of a uniaxial Lifshitz point is calculated at one-loop level using field-theoretic and $ε_{L}$-expansion methods. We use the Schwinger parametrization of the propagator in order to split the quadratic and quartic part of the momenta, as well as a new special symmetry point suitable for renormalization purposes. For a cubic lattice (d = 3), we find the result $\frac{C_{+}}{C_{-}} = 3.85$.
The Einstein-Proca action is known to have asymptotically locally Lifshitz spacetimes as classical solutions. For dynamical exponent z=2, two-point correlation functions for fluctuations around such a geometry are derived analytically. It is found that the retarded correlators are stable in the sense that all quasinormal modes are situated in the lower half-plane of complex frequencies. Correlators in the longitudinal channel exhibit features that are reminiscent of a structure usually obtained in field theories that are logarithmic, i.e. contain an indecomposable highest weight representation…
In this paper, we study static vacuum solutions of quantum gravity at a fixed Lifshitz point in (2+1) dimensions, and present all the diagonal solutions in closed forms in the infrared limit. The exact solutions represent spacetimes with very rich structures: they can represent generalized BTZ black holes, Lifshitz space-times or Lifshitz solitons, in which the spacetimes are free of any kind of space-time singularities, depending on the choices of the free parameters of the solutions. We also find several classes of exact static non-diagonal solutions, which represent similar space-time struc…
The presence of an isotropic tricritical Lifshitz point for the O(N) scalar theory is investigated in the 1/N expansion by means of the Functional Renormalization Group equations. At leading order, the non-trivial Lifshitz point is observed if the number of dimensions d is taken between d=4 and d=8, and the eigenvalue spectrum of the associated eigendirections is derived. At order 1/N, the anomalous dimension eta_N is computed and it is found to vanish both in d=4 and d=8, while it turns out to be positive between these two values, although strongly dependent on the choice of infrared regulato…
We study a minimally coupled charged scalar field in a charged Lifshitz background. For z=2, we find an analytic expression for the corresponding low energy retarded Green's function. Unlike the RN-AdS case, the position of the superfluid surfaces depends on the charge of the scalar field only through the IR scaling dimension. We show that by increasing the dynamical exponent, the dual theory becomes more stable. We also show that the background could suffer from an instability of the IR geometry leading to a bifurcating critical point. It also allows the existence of scalar hair, causing hybr…
In this paper, based on the principles of linear response theory, we compute the longitudinal DC conductivity associated with Lifshitz like fixed points in the presence of chiral anomalies in ($ 3+1 $) dimensions. In our analysis, apart from having the usual anomalous contributions due to chiral anomaly, we observe an additional and pure \textit{parity odd} effect to the magnetoconductivity which has its origin in the broken Lorentz (boost) invariance at a Lifshitz fixed point. We also device a holographic set up in order to compute ($ z=2 $) Lifshitz contributions to the magnetoconductivity p…
We study critical dynamics through time evolution of quantum field theories driven to a Lifshitz-like fixed point, with $z>1$, under relevant deformations. The deformations we consider are fast smooth quantum quenches, namely when the quench scale $δt^{-z}$ is large compared to the deformation scale. We show that in holographic models the response of the system merely depends on the scaling dimension of the quenched operator as $δλ\cdotδt^{d-2Δ+z-1}$, where $δλ$ is the deformation amplitude. This scaling behavior is enhanced logarithmically in certain cases. We also study free Lifshitz scalar …
We present the critical exponents $ν_{L2}$, $η_{L2}$ and $γ_{L}$ for an $m$-axial Lifshitz point at second order in an $ε_{L}$ expansion. We introduced a constraint involving the loop momenta along the $m$-dimensional subspace in order to perform two- and three-loop integrals. The results are valid in the range $0 \leq m < d$. The case $m=0$ corresponds to the usual Ising-like critical behavior.
A new renormalization group treatment is proposed for the critical exponents of an m-fold Lifshitz point. The anisotropic cases (m not equal 8) are described by two independent fixed points associated to two independent momentum flow along the quadratic and quartic directions, respectively. The isotropic case is described separately. In that case, the fixed point is due to renormalization group transformations along the quartic directions. The new scaling laws are derived for both cases and generalize the ones previously reported.
The critical exponents $ν_{L2}, η_{L2}$ and $γ_{L2}$ of a uniaxial Lifshitz point are calculated at two-loop level using renormalization group and $ε_{L}$-expansion techniques. We found a new constraint involving the loop momenta along the competition axis, which allows to solve the two-loop integrals. The exponent $γ_{L2}$ obtained using our method is in good agreement with numerical estimates based on Monte Carlo simulations.
We present type IIB supergravity solutions which are expected to be dual to certain Lifshitz-like fixed points with anisotropic scale invariance. They are expected to describe a class of D3-D7 systems and their finite temperature generalizations are straightforward. We show that there exist solutions that interpolate between these anisotropic solutions in the IR and the standard AdS5 solutions in the UV. This predicts anisotropic RG flows from familiar isotropic fixed points to anisotropic ones. In our case, these RG flows are triggered by a non-zero theta-angle in Yang-Mills theories that lin…
We show that holographic renormalization of relativistic gravity in asymptotically Lifshitz spacetimes naturally reproduces the structure of gravity with anisotropic scaling: The holographic counterterms induced near anisotropic infinity take the form of the action for gravity at a Lifshitz point, with the appropriate value of the dynamical critical exponent $z$. In the particular case of 3+1 bulk dimensions and $z=2$ asymptotic scaling near infinity, we find a logarithmic counterterm, related to anisotropic Weyl anomaly of the dual CFT, and show that this counterterm reproduces precisely the …
We study renormalization group flows in the Lifshitz-like $N$-flavour four fermi model discussed in 0905.2928. In the large-$N$ limit, a nontrivial flow occurs in only one of all possible marginal couplings and one relevant coupling, which provides the scale for Lorentz invariance violations. We discuss in detail the phase diagram and RG flows in the space of couplings, which includes the Lifshitz fixed point, the free field fixed point and a new fixed point characterized by $z=1$ scaling and a violation of Lorentz invariance, which cannot be tuned away by adjusting a parameter. In the broken …
We use the Wetterich equation for foliated spacetimes to study the RG flow of projectable Horava-Lifshitz gravity coupled to n Lifshitz scalars. Using novel results for anisotropic heat kernels, the matter-induced beta functions for the gravitational couplings are computed explicitly. The RG flow exhibits an UV attractive anisotropic Gaussian fixed point where Newton's constant vanishes and the extra scalar mode decouples. This fixed point ensures that the theory is asymptotically free in the large-n expansion, indicating that projectable Horava-Lifshitz gravity is perturbatively renormalizabl…
The large-n expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic d-dimensional systems at m-axial Lifshitz points. We derive the leading nontrivial 1/n correction for the perpendicular correlation-length exponent nu_{L2} and hence several related thermal exponents to order O(1/n). The results are consistent with known large-n expansions for d-dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension d^*=4+m/2 for generic m\in[0,d]. An…
The behaviour of the 3D axial next-nearest neighbour Ising (ANNNI) model at the uniaxial Lifshitz point is studied using Monte Carlo techniques. A new variant of the Wolff cluster algorithm permits the analysis of systems far larger than in previous studies. The Lifshitz point critical exponents are $α=0.18(2)$, $β=0.238(5)$ and $γ=1.36(3)$. Data for the spin-spin correlation function are shown to be consistent with the explicit scaling function derived from the assumption of local scale invariance, which is a generalization of conformal invariance to the anisotropic scaling {\em at} the Lifsh…
We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz point proposed by Ho${\rm\check{r}}$ava. Assuming power-counting renormalizability, foliation preserving diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational waves are circularly polarized due to parity violation. The chirality of primordial gravitational waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through observations of cosmic microwave background radiation and stochastic gravitational waves.
We calculate one-loop contributions to the two and three point spinor-vector functions in z=2 Horava-Lifshitz QED. This allows us to obtain the anomalous magnetic moment.
We show that three-dimensional massive gravity admits Lifshitz metrics with generic values of the dynamical exponent z as exact solutions. At the point z=3, exact black hole solutions which are asymptotically Lifshitz arise. These spacetimes are three-dimensional analogues of those that were recently proposed as gravity duals for scale invariant fixed points.
We introduce the Callan-Symanzik method in the description of anisotropic as well as isotropic Lifshitz critical behaviors. Renormalized perturbation theories are defined by normalization conditions with nonvanishing masses and at zero external momenta. The orthogonal approximation is employed to obtain the critical indices $η_{L2}$, $ν_{L2}$, $η_{L4}$ and $ν_{L4}$ diagramatically at least up to two-loop order in the anisotropic criticalities. This approximation is also utilized to compute the exponents $η_{L4}$ and $ν_{L4}$ in the isotropic case. Furthermore, we compute those exponents exactl…
We study the one-loop two point functions of the gauge, scalar and spinor fields for a Horava-Lifshitz-like QED with critical exponent $z=2$. It turns out that, in certain cases, the dynamical restoration of the Lorentz symmetry at low energies can take place. We also analyze the three point vertex function of the gauge and spinor fields and prove that the triangle anomaly identically vanishes in this theory.
We study scale-invariant systems in the presence of Gaussian quenched electric disorder, focusing on the tails of the energy spectra induced by disorder. For relevant disorder we derive asymptotic expressions for the densities of unit-charged states in the tails, positing the existence of saddle points in appropriate disorder integrals. The resultant scalings are dictated by spatial dimensions and dynamical exponents of the systems.
We study asymptotically Lifshitz spacetimes and the constraints on flows between Lifshitz fixed points imposed by the null energy condition. In contrast with the relativistic holographic c-theorem, where the effective AdS radius, L, is monotonically decreasing in the IR, for Lifshitz backgrounds we find that both L and z may flow in either direction. We demonstrate this with several numerical examples in a phenomenological model with a massive gauge field coupled to a real scalar.
The "pole-skipping" phenomenon reflects that the retarded Green's function is not unique at a pole-skipping point in momentum space $(ω,k)$. We explore the universality of the pole-skipping in different geometries. In holography, near horizon analysis of the bulk equation of motion is a simpler way to derive a pole-skipping point and we use this method in Lifshitz, AdS$_2$ and Rindler geometries. We also study the complex hydrodynamic analyses and find that the dispersion relations in terms of dimensionless variables $\fracω{2πT}$ and $\frac{\vert k\vert}{2πT}$ pass through pole-skipping point…
We introduce the electromagnetic-gravitational coupling in the Hořava-Lifshitz framework, in $3+1$ dimensions, by considering the Hořava-Lifshitz gravity theory in $4+1$ dimensions at the kinetic conformal point and then performing a Kaluza-Klein reduction to $3+1$ dimensions. The action of the theory is second order in time derivatives and the potential contains only higher order spacelike derivatives up to $z=4$, $z$ being the critical exponent. These terms include also higher order derivative terms of the electromagnetic field. The propagating degrees of freedom of the theory are exactly th…
I provide a broad framework to embed gradient flow equations in non-relativistic field theory models that exhibit anisotropic scaling. The prime example is the heat equation arising from a Lifshitz scalar field theory; other examples include the Allen-Cahn equation that models the evolution of phase boundaries. Then, I review recent results reported in arXiv:1002.0062 describing instantons of Horava-Lifshitz gravity as eternal solutions of certain geometric flow equations on 3-manifolds. These instanton solutions are in general chiral when the anisotropic scaling exponent is z=3. Some general …
The functional renormalization group equation for projectable Hořava-Lifshitz gravity is used to derive the non-perturbative beta functions for the Newton's constant, cosmological constant and anisotropy parameter. The resulting coupled differential equations are studied in detail and exemplary RG trajectories are constructed numerically. The beta functions possess a non-Gaussian fixed point and a one-parameter family of Gaussian fixed points. One of the Gaussian fixed points corresponds to the Einstein-Hilbert action with vanishing cosmological constant and constitutes a saddle point with one…
We use the holographic duality to study quantum quenches of a strongly coupled CFT that drive the theory towards a non-relativistic fixed point with Lifshitz scaling. We consider the case of a Lifshitz dynamical exponent $z$ close to unity, where the non-relativistic field theory can be understood as a specific deformation of the corresponding CFT and, hence, the standard holographic dictionary can be applied. On the gravity side this amounts to finding a dynamical bulk solution which interpolates between AdS and Lishitz spacetimes as time evolves. We show that an asymptotically Lifshitz black…
The critical behaviour of d-dimensional n-vector models at m-axial Lifshitz points is considered for general values of m in the large-n limit. It is proven that the recently obtained large-N expansions [J. Phys.: Condens. Matter 17, S1947 (2005)] of the correlation exponents η_{L2}, η_{L4} and the related anisotropy exponent θare fully consistent with the dimensionality expansions to second order in ε=4+m/2-d [Phys. Rev. B 62, 12338 (2000); Nucl. Phys. B 612, 340 (2001)] inasmuch as both expansions yield the same contributions of order ε^2/n.
