We investigate the scalar and tensor perturbations in Horava gravity, with and without detailed balance, around a flat background. Once both types of perturbations are taken into account, it is revealed that the theory is plagued by ghost-like scalar instabilities in the range of parameters which would render it power-counting renormalizable, that cannot be overcome by simple tricks such as analytic continuation. Implementing a consistent flow between the UV and IR limits seems thus more challenging than initially presumed, regardless of whether the theory approaches General Relativity at low energies or not. Even in the phenomenologically viable parameter space, the tensor sector leads to additional potential problems, such as fine-tunings and super-luminal propagation.
We investigate the Einstein static universe (ESU) and the emergent universe scenario in the framework of Hořava-Lifshitz-like $F(R)$ gravity. We first perform a dynamical analysis in the phase space, and amongst others we show that a spatially open universe filled with matter satisfying the strong energy condition can exhibit a stable static phase. Additionally, we examine the behavior of the scenario under scalar perturbations and extract the conditions under which it is free of perturbative instabilities, showing that the obtained background ESU solutions are free of such instabilities. Howe…
In this paper, we consider non-perturbative quantum correction which appears as exponential term in the black hole entropy. We study consequence thermodynamics of the Hořava-Lifshitz black hole at quantum scales. We consider two cases of Kehagius-Sfetsos and Lu-Mei-Pop solutions and investigate black hole stability. We find that non-perturbative quantum correction yields to an instability at infinitesimal horizon radius of Kehagius-Sfetsos solution. On the other hand, non-perturbative quantum correction yields to the stability of Lu-Mei-Pop solution. Hence, we find that holographic dual of Lu-…
We perform a non-perturbative analysis to the Hamiltonian constraint of the lowest-order effective action of the complete Horava theory, which includes a (\partial_i \ln N)^2 term in the Lagrangian. We cast this constraint as a partial differential equation for N and show that the solution exists and is unique under a condition of positivity for the metric and its conjugate momentum. We interpret this condition as the analog of the positivity of the spatial scalar curvature in general relativity. From the analysis we extract several general properties of the solution for N: an upper bound on i…
We present a well-tempered DeWitt wave function, which vanishes at the classical big-bang singularity, in Hořava-Lifshitz (HL) cosmology with tensor perturbation, both analytically and numerically. In general relativity, the DeWitt wave function is ill-behaved once the tensor perturbation is taken into account. This is essentially because the amplitude of the perturbation diverges at the singularity and the perturbative expansion completely breaks down. On the other hand, in HL gravity it is known that the higher dimensional operators required by the perturbative renormalizability render the t…
We study the modifications induced by spacetime anisotropy on the Casimir effect in the case of two parallel plates. Nonperturbative and perturbative regimes are analyzed. In the first case the Casimir force either vanishes or it reverses its direction which, in any case, makes the proposal untenable. On the other hand, the perturbative model enables us to incorporate appropriately the effects of spacetime anisotropy.
A lattice regularization for the $2$d projectable Horava-Lifshitz (HL) quantum gravity is known to be the $2$d causal dynamical triangulations (CDT), and the $2$d CDT can be generalized so as to include all possible genus contributions non-perturbatively. We show that in the context of HL gravity, effects coming from such a non-perturbative sum over topologies can be successfully taken into account, if we quantize the $2$d projectable HL gravity with a simple bi-local wormhole interaction. This conference paper is based on the article, Phys. Lett. B 816 (2021), 136205.
We consider scalar perturbations in the time-dependent Hourava-Witten Model in order to probe its stability. We show that during the non-singular epoque the model evolves without instabilities until it encounters the curvature singularity where a big crunch is supposed to occur. We compute the frequencies of the scalar field oscillation during the stable period and show how the oscillations can be used to prove the presence of such a singularity.
We consider the branch of the projectable Horava-Lifshitz model which exhibits ghost instabilities in the low energy limit. It turns out that, due to the Lorentz violating structure of the model and to the presence of a finite strong coupling scale, the vacuum decay rate into photons is tiny in a wide range of phenomenologically acceptable parameters. The strong coupling scale, understood as a cutoff on ghosts' spatial momenta, can be raised up to $Λ\sim 10$ TeV. At lower momenta, the projectable Horava-Lifshitz gravity is equivalent to General Relativity supplemented by a fluid with a small p…
We present a fully nonlinear study of long wavelength cosmological perturbations within the framework of the projectable Horava-Lifshitz gravity, coupled to a single scalar field. Adopting the gradient expansion technique, we explicitly integrate the dynamical equations up to any order of the expansion, then restrict the integration constants by imposing the momentum constraint. While the gradient expansion relies on the long wavelength approximation, amplitudes of perturbations do not have to be small. When the $λ\to 1$ limit is taken, the obtained nonlinear solutions exhibit a continuous beh…
We consider Horava gravity coupled to Maxwell and higher derivative magnetic terms. We construct static spherically symmetric black hole solutions in the low-energy approximation. We calculate the horizon locations and temperatures in the near-extremal limit, for asymptotically flat and (anti-)de Sitter spaces. We also construct a detailed balanced version of the theory, for which we find projectable and non-projectable, non-perturbative solutions.
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…
Causal Dynamical Triangulations (CDT) is a non-perturbative quantisation of general relativity. Hořava-Lifshitz gravity on the other hand modifies general relativity to allow for perturbative quan- tisation. Past work has given rise to the speculation that Hořava-Lifshitz gravity might correspond to the continuum limit of CDT. In this paper we add another piece to this puzzle by applying the CDT quantisation prescription directly to Hořava-Lifshitz gravity in 2 dimensions. We derive the continuum Hamiltonian and we show that it matches exactly the Hamiltonian one derives from canonically quant…
By studying perturbations about the vacuum, we show that Horava gravity suffers from two different strong coupling problems, extending all the way into the deep infra-red. The first of these is associated with the principle of detailed balance and explains why solutions to General Relativity are typically not recovered in models that preserve this structure. The second of these occurs even without detailed balance and is associated with the breaking of diffeomorphism invariance, required for anisotropic scaling in the UV. Since there is a reduced symmetry group there are additional degrees of …
We address the consistency of Horava's proposal for a theory of quantum gravity from the low-energy perspective. We uncover the additional scalar degree of freedom arising from the explicit breaking of the general covariance and study its properties. The analysis is performed both in the original formulation of the theory and in the Stueckelberg picture. A peculiarity of the new mode is that it satisfies an equation of motion that is of first order in time derivatives. At linear level the mode is manifest only around spatially inhomogeneous and time-dependent backgrounds. We find two serious p…
A proposal for a power-counting renormalizable theory of quantum gravity at a Lifshitz point was recently put forth by Horava (arXiv:0901.3775), and has been since dubbed as Horava-Lifshitz gravity. The theory explicitly breaks Lorentz invariance, which introduces an apparent extra scalar degree of freedom. In this note, we show that the low energy limit of (non-projectible) Horava-Lifshitz gravity is uniquely given by the quadratic cuscuton model: a covariant scalar field theory with an infinite speed of sound and a quadratic potential, which is minimally coupled to Einstein gravity. This imp…
Horava gravity has been constructed so as to exhibit anisotropic scaling in the ultraviolet, as this renders the theory power-counting renormalizable. However, when coupled to matter, the theory has been shown to suffer from quadratic divergences. A way to cure these divergences is to add terms with both time and space derivatives. We consider this extended version of the theory in detail. We perform a perturbative analysis that includes all modes, determine the propagators and discuss how including mixed-derivative terms affects them. We also consider the Lifshitz scalar with mixed-derivative…
We prove perturbative renormalizability of projectable Horava gravity. The key element of the argument is the choice of a gauge which ensures the correct anisotropic scaling of the propagators and their uniform falloff at large frequencies and momenta. This guarantees that the counterterms required to absorb the loop divergences are local and marginal or relevant with respect to the anisotropic scaling. Gauge invariance of the counterterms is achieved by making use of the background-covariant formalism. We also comment on the difficulties of this approach when addressing the renormalizability …
In an earlier article [arXiv:0902.0590 [hep-th], Phys. Rev D80 (2009) 025011], I discussed the potential benefits of allowing Lorentz symmetry breaking in quantum field theories. In particular I discussed the perturbative power-counting finiteness of the normal-ordered :P(phi)^{z>=d}_{d+1}: scalar quantum field theories, and sketched the implications for Horava's model of quantum gravity. In the current rather brief addendum, I will tidy up some dangling issues and fill out some of the technical details of the argument indicating the power-counting renormalizability of a z>=d variant of Horava…
We find stable singularity-free cosmological solutions in non-flat Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime in the context of Hořava-Lifshitz (HL) theory. Although we encounter the negative squared effective masses of the scalar perturbations in the original HL theory, the behaviors can be remedied by relaxing the projectability condition. In our analysis, the effects from the background dynamics are taken into account as well as the sign of the coefficients in the quadratic action for perturbations. More specifically, we give further classification of the gradient stability/instab…
We compare the initial value formulation of the low-energy limit of (non-projectable) Horava gravity to that of Einstein-aether theory when the aether is assumed to be hypersurface orthogonal at the level of the field equations. This comparison clearly highlights a crucial difference in the causal structure of the two theories at the non-perturbative level: in Horava gravity evolution equations include an elliptic equation that is not a constraint relating initial data but needs to be imposed on each slice of the foliation. This feature is absent in Einstein-aether theory. We discuss its physi…
This article reviews basic construction and cosmological implications of a power-counting renormalizable theory of gravitation recently proposed by Horava. We explain that (i) at low energy this theory does not exactly recover general relativity but instead mimic general relativity plus dark matter; that (ii) higher spatial curvature terms allow bouncing and cyclic universes as regular solutions; and that (iii) the anisotropic scaling with the dynamical critical exponent z=3 solves the horizon problem and leads to scale-invariant cosmological perturbations even without inflation. We also comme…
We consider a Horava theory that has a consistent structure of constraints and propagates two physical degrees of freedom. The Lagrangian includes the terms of Blas, Pujolas and Sibiryakov. The theory can be obtained from the general Horava's formulation by setting lambda = 1/3. This value of lambda is protected in the quantum formulation of the theory by the presence of a constraint. The theory has two second-class constraints that are absent for other values of lambda. They remove the extra scalar mode. There is no strong-coupling problem in this theory since there is no extra mode. We perfo…
Horava gravity is a proposal for completing general relativity in the ultraviolet by interactions that violate Lorentz invariance at very high energies. We focus on (2+1)-dimensional projectable Horava gravity, a theory which is renormalizable and perturbatively ultraviolet-complete, enjoying an asymptotically free ultraviolet fixed point. Adding a small cosmological constant to regulate the long distance behavior of the metric, we search for all circularly symmetric stationary vacuum solutions with vanishing angular momentum and approaching the de Sitter metric with a possible angle deficit a…
We present a one loop calculation in the context of Horava-Lifshitz gravity. Due to the complexity of the calculation in the full theory we focus here on the study of a toy model, namely the conformal reduction of the z=2 projectable theory in 2+1 dimensions. For this value of the dimension there are no gravitons, hence the conformal mode is the only physical degree of freedom, and thus we expect our toy model to lead to qualitatively correct answers regarding the perturbative renormalization of the full theory. We find that Newton's constant (dimensionless in Horava-Lifshitz gravity) is asymp…
We study possible links between quantum gravity phenomenology encoding Lorentz violations as nonlinear dispersions, the Einstein-Finsler gravity models, EFG, and nonholonomic (non-integrable) deformations to Hořava-Lifshitz, HL, and/or Einstein's general relativity, GR, theories. EFG and its scaling anisotropic versions formulated as Hořava-Finsler models, HF, are constructed as covariant metric compatible theories on (co) tangent bundle to Lorentz manifolds and respective anisotropic deformations. Such theories are integrable in general form and can be quantized following standard methods of …
Horava gravity breaks Lorentz symmetry by introducing a dynamical timelike scalar field (the khronon), which can be used as a preferred time coordinate (thus selecting a preferred space-time foliation). Adopting the khronon as the time coordinate, the theory is invariant only under time reparametrizations and spatial diffeomorphisms. In the infrared limit, this theory is sometimes referred to as khronometric theory. Here, we explicitly construct a generalization of khronometric theory, which avoids the propagation of Ostrogradski modes as a result of a suitable degeneracy condition (although s…
In this short note we compare the endpoint of tachyon condensation of twisted circles with the endpoint of nonpertubative brane nucleation in the Kaluza-Klein Melvin spacetime.
We derive a universal thermal effective potential, which describes all possible high-temperature instabilities of the known N=4 superstrings, using the properties of gauged N=4 supergravity. These instabilities are due to three non-perturbative thermal dyonic modes, which become tachyonic in a region of the thermal moduli space. The latter is described by three moduli, s,t,u, which are common to all non-perturbative dual-equivalent strings with N=4 supersymmetry in five dimensions: the heterotic on T^4xS^1, the type IIA on K3xS^1, the type IIB on K3xS^1 and the type I on T^4x S^1. The non-pert…
Horava's proposal for non-relativistic quantum gravity introduces a preferred time foliation of space-time which violates the local Lorentz invariance. The foliation is encoded in a dynamical scalar field which we call `khronon'. The dynamics of the khronon field is sensitive to the symmetries and other details of the particular implementations of the proposal. In this paper we examine several consistency issues present in three non-relativistic gravity theories: Horava's projectable theory, the healthy non-projectable extension, and a new extension related to ghost condensation. We find that …
We obtain the non-perturbative effective potential for the dual five-dimensional N=4 strings in the context of finite-temperature regarded as a breaking of supersymmetry into four space-time dimensions. Using the properties of gauged N=4 supergravity we derive the universal thermal effective potential describing all possible high-temperature instabilities of the known N=4 superstrings. These strings undergo a high-temperature transition to a new phase in which five-branes condense. This phase is described in detail, using both the effective supergravity and non-critical string theory in six di…
It is widely accepted that moduli in the mass range 10eV - $10^4$GeV which start to oscillate with an amplitude of the order of the Planck scale either jeopardize successful predictions of nucleosynthesis or overclose the Universe. It is shown that the moduli problem can be relaxed by making use of parametric resonance. A new non-perturbative decay channel for moduli oscillations is discussed. This channel becomes effective when the oscillating field results in a net negative mass term for the decay products. This scenario allows for the decay of the moduli much before nucleosynthesis and, the…
It is argued that the quadratic and linear non-commutative IR divergences that occur in U(1) theory on non-commutative Minkowski spacetime for small non-commutativity matrices $θ^{μν}$ are gauge-fixing independent. This implies in particular that the perturbative tachyonic instability produced by the quadratic divergences of this type in the vacuum polarization tensor is not a gauge-fixing artifact. Supersymmetry can be introduced to remove from the renormalized Green functions at one loop, not only the non-logarithmic non-commutative IR divergences, but also all terms proportional to $θ^{μν}p…
We study one-loop corrections in scalar and gauge field theories on the non-commutative torus. For rational theta, Morita equivalence allows these theories to be reformulated in terms of ordinary theories on a commutative torus with twisted boundary conditions. UV/IR mixing does not lead to singularities, however there can be large corrections. In particular, gauge theories show tachyonic instabilities for some of the modes. We discuss their relevance to spontaneous Z_N x Z_N symmetry breaking in the Morita dual SU(N) theory due to electric flux condensation.
Using the properties of gauged N=4 supergravity, we show that it is possible to derive a universal thermal effective potential that describes all possible high-temperature instabilities of the known N=4 superstrings. These instabilities are due to non-perturbative dyonic modes, which become tachyonic in a region of the thermal moduli space M={s,t,u}; M is common to all non-perturbative dual-equivalent N=4 superstrings in five dimensions. We analyse the non-perturbative thermal potential and show the existence of a phase transition at high temperatures corresponding to a condensation of 5-brane…
In this paper we suggest a new source of perturbative decay of the KPV-state, which might have consequences for the viability of the KKLT-construction. The results do not rely on any direct enhancement of the decay due to flux accumulating on the anti-brane in transverse space. Instead, we note that the system can lower its energy through a sequence of NS5-configurations all the way to the true vacuum, without encountering a barrier, if we allow for clumping of screened charge in space time. The clumping can possibly be a parallel to the Gregory-Laflamme instability of black branes. The result…
We extend the study of the non-linear perturbative theory of weakly turbulent energy cascades in AdS$_{d+1}$ to include solutions of driven systems, i.e. those with time-dependent sources on the AdS boundary. This necessitates the activation of non-normalizable modes in the linear solution for the massive bulk scalar field, which couple to the metric and normalizable scalar modes. We determine analytic expressions for secular terms in the renormalization flow equations for any mass, and for various driving functions. Finally, we numerically evaluate these sources for $d = 4$ and discuss what r…
Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)（马克斯·普朗克物理研究所（维尔纳·海森堡研究所））；Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova, and I.N.F.N. Sezione di Padova（帕多瓦大学伽利略·伽利莱物理与天文学系及意大利国家核物理研究所帕多瓦分部）
We compactify M-theory in the Horava-Witten formulation on S^1/Z_2 \times K3 \times T^2. Focusing on the moduli-space of vector multiplets of the resulting four-dimensional N=2 theory, we determine the prepotential as an expansion in two dimensionless parameters which both scale as κ^{2/3}. We determine the prepotential completely to relative order κ^{4/3} and compare the expression with the results obtained for the perturbative string theories. We find complete agreement to relative order κ^{4/3} between the strong and weak coupling regimes. The sources of higher order perturbative and non-pe…
We performed a study of the perturbative instabilities in Einstein-Maxwell-Chern-Simons theory with a gravitational Chern-Simons term, which is dual to a strongly coupled field theory with both chiral and mixed gauge-gravitational anomaly. With an analysis of the fluctuations in the near horizon regime at zero temperature, we found that there might be two possible sources of instabilities. The first one corresponds to a real mass-squared which is below the BF bound of AdS$_2$, and it leads to the bell-curve phase diagram at finite temperature. The effect of mixed gauge-gravitational anomaly is…
We discuss the perturbative expansion of SU(N) Yang-Mills theories defined on a d-dimensional torus of linear size l with twisted boundary conditions, generalizing previous results in the literature. For a specific class of twist tensors depending on a single integer flux value k, we show that perturbative results to all orders depend on the combination lN^(2/d) and a flux-dependent angle theta. This implies a new kind of volume independence that holds at finite N and for fixed values of theta. Our results also provide interesting information about the possible occurrence of tachyonic instabil…
We examine the consequences of Lorentz violation during slow-roll inflation. We consider a canonical scalar inflaton coupled, through its potential, to the divergence of a fixed-norm timelike vector field, or "aether." The vector is described by Einstein-aether theory, a vector-tensor model of gravitational Lorentz violation. We derive and analyze the cosmological perturbation equations for the metric, inflaton, and aether. If the scale of Lorentz violation is sufficiently small compared to the Planck mass, and the strength of the scalar-aether coupling is suitably large, then the spin-0 and s…
We discuss two types of instabilities which may arise in string theory compactified to asymptotically AdS spaces: perturbative, due to discrete modes in the spectrum of the Laplacian, and non-perturbative, due to brane nucleation. In the case of three dimensional Einstein manifolds, we completely characterize the presence of these instabilities, and in higher dimensions we provide a partial classification. The analysis may be viewed as an extension of the Breitenlohner-Freedman bound. One interesting result is that, apart from a very special class of exceptions, all Euclidean asymptotically Ad…
n-DBI gravity is a gravitational theory which yields near de Sitter inflation spontaneously at the cost of breaking Lorentz invariance by a preferred choice of foliation. We show that this breakdown endows n-DBI gravity with one extra physical gravitational degree of freedom: a scalar graviton. Its existence is established by Dirac's theory of constrained systems. Firstly, studying scalar perturbations around Minkowski space-time, we show that there exists one scalar degree of freedom and identify it in terms of the metric perturbations. Then, a general analysis is made in the canonical formal…
We investigate perturbative aspects of gravity with a general F(R) Lagrangian, as well as nonperturbative dilatonic solutions. For the first part, we are interested in stability and the definition of asymptotic charges. The main result of this study is that, while generic F(R) theories are stable under metric perturbations, they are expected to show instabilities against curvature perturbations when the Lagrangian includes 1/R terms. For the second part, one is interested on exact solutions, and we explicitly construct kink-like solutions of the Liouville type for the dilaton field for F(R) ha…
In this paper, we study a class of higher derivative, non-local gravity which admits homogeneous and isotropic non-singular, bouncing universes in the absence of matter. At the linearized level, the theory propagates only a scalar degree of freedom, and no vector or tensor modes. The scalar can be made free from perturbative ghost instabilities, and has oscillatory and bounded evolution across the bounce.
Resumming quantum fluctuations at the level of the gravitational path integral is expected to result in non-local effective actions and thus in a non-trivial momentum dependence of the propagator. Which properties the (dressed) graviton propagator has to satisfy and whether they can all be met are key open questions. In this work we present criteria and conditions for the momentum dependence of a graviton propagator which is consistent with unitarity, causality, and stability in a non-perturbative setting. To this end, we revisit several aspects of these conditions, highlighting some caveats a…
The authors of arXiv:1610.01533 have recently proposed a stronger version of the weak gravity conjecture (WGC), based on which they concluded that all those non-supersymmetric AdS vacua that can be embedded within a constistent theory of quantum gravity necessarily develop instabilities. In this paper we further elaborate on this proposal by arguing that the aforementioned instabilities have a perturbative nature and arise from the crucial interplay between the closed and the open string sectors of the theory.
Recently, Saad, Shenker and Stanford showed how to define the genus expansion of Jackiw-Teitelboim quantum gravity in terms of a double-scaled Hermitian matrix model. However, the model's non-perturbative sector has fatal instabilities at low energy that they cured by procedures that render the physics non-unique. This might not be a desirable property for a system that is supposed to capture key features of quantum black holes. Presented here is a model with identical perturbative physics at high energy that instead has a stable and unambiguous non-perturbative completion of the physics at lo…
The quantum dynamics of the symmetry broken lambda (Phi^2)^2 scalar field theory in the presence of an homogeneous external field is investigated in the large N limit. We choose as initial state the ground state for a constant external field J .The sign of the external field is suddenly flipped from J to - J at a given time and the subsequent quantum dynamics calculated. Spinodal instabilities and parametric resonances produce large quantum fluctuations in the field components transverse to the external field. This allows the order parameter to turn around the maximum of the potential for inte…
We discuss non-perturbative instabilities, mediated by bubbles of nothing, in the context of the AdS/CFT correspondence. By exploring the phase diagram of such decays we give an interpretation of the process in terms of an effective potential in a quantum mechanics of a single variable, a winding mode condensate. The decay corresponds to a conventional first order transition, the true vacuum being a non-geometrical "nothing" state.
We study the cosmology of a toy modified theory of gravity in which gravity shuts off at short distances, as in the fat graviton scenario of Sundrum. In the weak-field limit, the theory is perturbatively local, ghost-free and unitary, although likely suffers from non-perturbative instabilities. We derive novel self-inflationary solutions from the vacuum equations of the theory, without invoking scalar fields or other forms of stress energy. The modified perturbation equation expressed in terms of the Newtonian potential closely resembles its counterpart for inflaton fluctuations. The resulting…
