Massive Modes Research Articles

Massive quasinormal mode in the holographic Lifshitz theory

We investigate the holographic renormalization of the Einstein-Maxwell-dilaton theory which provides an asymptotic Lifshitz geometry dual to a Lifshitz field theory. In this case, the existence of a field combination with zero scaling dimension causes an ambiguity in fixing local counter terms. Nevertheless, we show that all possible local counter terms give rise to consistent thermodynamic quantities with the Lifshitz black brane results. In addition, we also study the retarded Green functions of the current and momentum operator of a non-relativistic Lifshitz field theory. In the non-zero momentum regime, the results show intriguingly that there exists a massive quasi-normal mode whose effective mass is linearly proportional to temperature and that even at zero temperature there exists a quasi-normal mode in the non-relativistic Lifshitz medium.

New analytical solutions for bosonic field trapping in thick branes

New analytical solutions for gravity, scalar and vector field localization in Randall–Sundrum (RS) models are found. A smooth version of the warp factor with an associated function f(z)=exp(3A(z)/2) inside the walls (|z|<d) is defined, leading to an associated equation and physical constraints on the continuity and smoothness of the background resulting in a new space of analytical solutions. We solve this associated equation analytically for the parabolic and Pöschl–Teller potentials and analyze the spectrum of resonances for these fields. By using the boundary conditions we are able to show that, for any of these solutions, the density probability for finding a massive mode in the membrane has a universal behavior for small values of mass given by |ψm(0)|2=β1m+β3m3+βLm3log(m)+⋯. As a consequence, the form of the leading order correction, for example, to the Newton's law is general and does not depend on the potential used. At the end we also discuss why complications arise when we use the method to find analytical solutions to the fermion case.

Vector and fermion fields on a bouncing brane with a decreasing warp factor in a string-like defect

In a recent work, a model has been proposed where a brane is made of a scalar field with bounce-type configurations and embedded in a bulk with a string-like metric. This model produces an AdS scenario where the components of the energy–momentum tensor are finite and have its positivity ensured by a suitable choice of the bounce configurations. In the present work, we study the issue of gauge and fermion field localization in this scenario. In contrast with the five-dimensional case here the gauge field is localized without the dilaton contribution. Nevertheless, it is remarkable that the localization of the fermion field depends on the introduction of a minimal coupling with the angular component of the gauge field, which differs clearly from five-dimensional scenarios. Furthermore, we perform a qualitative analysis of the fermionic massive modes and conclude that only left-handed fermions could be localized in the brane.

Mass hierarchy, mass gap and corrections to Newton’s law on thick branes with Poincaré symmetry

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schroedinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with m^2>0, in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to compute the corrections to Newton's law in the thin brane limit. In the first case we consider a solution with a mass gap in the spectrum of KK fluctuations with two bound states - the massless 4D graviton free of tachyonic instabilities and a massive KK excitation - as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the (thin) Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved as in the Lykken-Randall model and the model is completely free of naked singularities.

Massless Modes and Abelian Gauge Fields in Multi-Band Superconductors

In $N$-band superconductors, the $U(1)^N$ phase invariance is spontaneously broken. We propose a model for $N$-band superconductors where the phase differences between gaps are represented by abelian gauge fields. This model corresponds to an $SU(N)$ gauge theory with the abelian projection. We show that there are massless modes as well as massive modes when the number of gaps $N$ is greater than 3. There are $N-3$ massless modes and two massive modes near a minimum of the Josephson potential when $N$ bands are equivalent and Josephson couplings are frustrated. The global symmetry $U(1)^{N-1}$ is broken down by the Josephson term to $U(1)^{N-3}$. A non-trivial configuration of the gauge field, that is, a monopole singularity of the gauge field results in a fractional quantum-flux vortex. The fractional quantum-flux vortex corresponds to a monopole in superconductors.

Four-dimensional gravity on supersymmetric dilatonic domain walls

We investigate the localization of four-dimensional metastable gravity in supersymmetric dilatonic domain walls through massive modes by considering several scenarios in the model. We compute corrections to the Newtonian potential for small and long distances compared with a crossover scale given in terms of the dilatonic coupling. 4D gravity behavior is developed on the brane for distance very much below the crossover scale, while for distance much larger, the 5D gravity is recovered. Whereas in the former regime gravity is always attractive, in the latter regime due to non-normalizable unstable massive graviton modes present on the spectrum, in some special cases, gravity appears to be repulsive and signals a gravitational confining phase which is able to produce an inflationary phase of the Universe.

Oscillatory features in the curvature power spectrum after a sudden turn of the inflationary trajectory

In the context of two-field inflation characterized by a light direction and a heavy direction, we revisit the question of the impact of the massive modes on the power spectrum produced after a turn in the inflationary trajectory. We consider in particular the resonant effect due to the background oscillations following a sharp turn. Working in the mass basis, i.e. in the basis spanned by the eigenvectors of the effective mass matrix for the perturbations, we provide an analytical estimate of the resonant effect, using the in-in formalism. In comparison with earlier estimates, we find the same the spectral dependence but a smaller amplitude. We also compute, again via the in-in formalism, the effect of the direct coupling between the light and heavy modes at the instant of the turn and confirm our previous results obtained via a different method.

LOOP VARIABLES AND GAUGE INVARIANT EXACT RENORMALIZATION GROUP EQUATIONS FOR CLOSED STRING THEORY

We formulate the Exact Renormalization Group on the string worldsheet for closed string backgrounds. The same techniques that were used for open strings are used here. There are some subtleties. One is that holomorphic factorization of the closed string vertex operators does not hold in the presence of a cutoff on the Euclidean worldsheet. This introduces extra terms in the Lagrangian at the cutoff scale and they turn out to be crucial for implementing gauge invariance. This naive generalization from open string to closed string requires a massive graviton and the gauge symmetry is Abelian, just as in open string theory. Interestingly, it turns out that if one introduces a nondynamical background metric (as in background field formalism) and combines a gauge transformation on the field with a transformation on the coordinates and background metric, the graviton can be massless. Some examples of background coordinate covariant equations are worked out explicitly. A preliminary discussion of massive modes, massive gauge transformations and the role of worldsheet regulator terms is given. Some of the gauge transformations can be given a geometric meaning if space–time is assumed to be complex at some level.

Zwei-Dreibein Gravity: A Two-Frame-Field Model of 3D Massive Gravity

We present a generally covariant and parity-invariant two-frame field ("zwei-dreibein") action for gravity in three space-time dimensions that propagates two massive spin-2 modes, unitarily, and we use Hamiltonian methods to confirm the absence of unphysical degrees of freedom. We show how zwei-dreibein gravity unifies previous "3D massive gravity" models and extends them, in the context of the AdS/CFT correspondence, to allow for a positive central charge consistent with bulk unitarity.

Dirac quasinormal modes in spherically symmetric regular black holes

Using the WKB approximation, massless and massive Dirac quasinormal modes (QNMs) are studied in spherically symmetric regular spacetimes. We analyze the relationships between QNM frequencies and the parameters (angular momentum number $l$, magnetic monopole charge $\ensuremath{\beta}$, and the mass of the field $m$) and discuss the extreme charge of magnetic monopole ${\ensuremath{\beta}}_{e}$ for spherically symmetric regular black holes. Furthermore, we apply an expansion method to expand QNMs in inverse powers of $L=l+1/2$ and confirm good precision with $l&gt;n$. Finally, we improve the traditional finite difference method to be available in the massive Dirac case and illuminate the dynamical evolution of the massive Dirac field.

Stability of vacua in new massive gravity in different gauges

We consider AdS3 and warped AdS3 vacua in new massive gravity and study the highest weight modes and general propagating modes as a set of solutions for the linearized equations of motion. We observed that depending on the choice of gauge there are two types of solutions. We show that for warped AdS3 vacuum, the massless modes which appear only in the harmonic gauge have zero energy density and do not get higher curvature corrections. By computing the energy density it can be shown that all massive modes have negative energy density. Our computations prove that the massive modes in warped AdS3 cannot be excluded by an appropriate boundary condition and this makes the theory unstable.

Kalb–Ramond field localization on the Bloch brane

This work deals with new results on the Kalb-Ramond (KR) field localization in braneworld models. We consider a five-dimensional warped spacetime with an embedded 4D thick brane which is generated by two real scalar fields coupled with gravity (the so called Bloch brane). We find a KR field zero mode localized with the inclusion of the dilaton coupling. Analyzing the massive spectrum, we detected a series of resonant modes that arise from the solutions of the Schr\"odinger-like equation for KR field. The effects of the brane thickness and of the dilaton coupling over the resonance structures are determined. Such analysis is extended to the resonance lifetimes of the massive modes, allowing a better understanding on the localization mechanism of the model.

The all-loop integrable spin-chain for strings on AdS3 × S 3 × T 4: the massive sector

We bootstrap the all-loop dynamic S-matrix for the homogeneous psu(1,1|2)^2 spin-chain believed to correspond to the discretization of the massive modes of string theory on AdS_3 x S^3 x T^4. The S-matrix is the tensor product of two copies of the su(1|1)^2 invariant S-matrix constructed recently for the d(2,1;alpha)^2 chain, and depends on two antisymmetric dressing phases. We write down the crossing equations that these phases have to satisfy. Furthermore, we present the corresponding Bethe Ansatz, which differs from the one previously conjectured, and discuss how our construction matches several recent perturbative calculations.

Quasinormal Modes of Hayward Regular Black Hole

In this paper, using asymptotic iteration method and eikonal limit, the massive scalar quasinormal modes (QNM) is studied in regular Hayward spacetime, which is much similar to Schwarzschild black hole when r→∞ but there is no singularity at the center. We analyze the QNM frequencies ω by varying the parameter β (it is related to mass of black hole and cosmological constant), spherical harmonic index L and the mass of scalar field m. The results show that the effect of β could lead to the real part of ω increase but the imaginary part decrease, which imply that the existence of cosmological constant would impact on the process of a black hole relaxing after it has been perturbed.

Solutions of massive gravity theories in constant scalar invariant geometries

We solve massive gravity field equations in the framework of locally homogenous and vanishing scalar invariant (VSI) Lorentzian spacetimes, which in three dimensions are the building blocks of constant scalar invariant (CSI) spacetimes. At first, we provide an exhaustive list of all Lorentzian three-dimensional homogeneous spaces and then we determine the Petrov type of the relevant curvature tensors. Among these geometries we determine for which values of their structure constants they are solutions of the field equations of massive gravity theories with a cosmological constant. The homogeneous solutions obtained are all of various Petrov types: , , II, III, Dt, Ds, N, O; the VSI geometries which we found are of Petrov type III. The Petrov types II and III are new explicit CSI space-time solutions of these types. We also examine the conditions under which the obtained anti-de Sitter solutions are free of tachyonic massive graviton modes.

Gauge vector field localization on a 3-brane placed in a warped transverse resolved conifold

We have investigated the features of the gauge vector field in a braneworld scenario built as a warped product between a 3-brane and a 2-cycle of the resolved conifold. This scenario allowed us to study how the gauge field behaves when the transverse manifold evolves upon a geometric flow that controls the singularity at the origin. Besides, since the transverse manifold has a cylindrical symmetry according to the 3-brane, this geometry can be regarded as a near brane correction of the string-like branes. Indeed, by means of a new warp function and the angular metric component of the resolved conifold, the braneworld can exhibit a conical form near the origin as well as a regular behavior in that region. The analysis of the gauge field in this background has been carried out for the s-wave state and a normalizable massless mode was found. For the massive modes, the resolution parameter avoids an infinite well on the brane and controls the depth of the well and the high of the barrier around the brane. The massive modes are slightly changed near the brane but they agreed with the string-like spectrum for large distances.

Closed flux tubes in higher representations and their string description in D=2+1 SU(N) gauge theories

We calculate, numerically, the low-lying spectrum of closed confining flux tubes that carry flux in different representations of SU(N). We do so for SU(6) at β = 171, where the calculated low-energy physics is very close to the continuum limit and, in many respects, also close to N = ∞. We focus on the adjoint, 84, 120, k = 2A, 2S and k = 3A,3M,3S representations and provide evidence that the corresponding flux tubes, albeit mostly unstable, do in fact exist. We observe that the ground state of a flux tube with momentum along its axis appears to be well defined in all cases and is well described by the Nambu-Goto spectrum (in flat space-time), all the way down to very small lengths, just as it is for flux tubes carrying fundamental flux. Excited states, however, typically show very much larger deviations from Nambu-Goto than the corresponding excitations of fundamental flux tubes and, indeed, cannot be extracted in many cases. We discuss whether what we are seeing here are separate stringy and massive modes or simply large corrections to energy levels that will become string-like at larger lengths.

Charged Quasinormal Modes and Dynamical Property of Black Hole with Global Monopole in de Sitter Spacetime

According to the basic rules of finite difference method,we calculate massive charged scalar field quasinormal modes of Reissner-Nordstrom-de Sitter Black Hole with a global monopole, which shows that when electronic quantity of scalar field e is comparatively small, all the factors including angular quantum number, the mass of scalar field, the size of horizon and the breaking scale will influence the frequency spectrum of quasinormal modes. When e is more than some definite critical value, second-order transition will appear and after that the curve of frequency spectrum rises, the black hole is no longer steady, which means when e is greater than some definite critical value, the structure of black hole can be changed. While the size of angular quantum number and breaking scale will influence the happening time of second-order transition. When breaking scale is less than some definite critical value, the second-order transition can be vanished.

Localization of bulk matter fields, the hierarchy problem and corrections to Coulomb’s law on a pure de Sitter thick braneworld

In this paper we investigate the localization and mass spectra of various matter fields with spin 0, 1 and $1/2$ on a geometric thick brane generated by pure four-dimensional (4D) and five-dimensional positive cosmological constants without bulk scalar fields. This model possesses a 4D cosmological constant that can be made as small as one desires without fine-tuning it with the bulk cosmological constant. The Randall-Sundrum model was obtained as an analytic continuation of the flat brane limit of this braneworld configuration when the Hubble parameter disappears. We also show that within the framework of this inflating braneworld model, it is possible to formulate a mechanism for obtaining TeV mass scales from Planck ones by adding a positive thin brane, where the Standard Model fields are trapped, located at a distance ${y}_{2}$ from the origin, where the Planck thick brane resides. The brane separation must be of the same order as the inverse thickness parameter of the model in order for the mechanism to generate the desired hierarchy. This result is obtained by imposing the recovery of both the correct 4D gravitational couplings and the actually observed accelerated expansion of the Universe in our de Sitter braneworld. Regarding the localization of matter in the purely geometric thick braneworld, for spin-0 massless and massive scalar fields as well as for spin-1 vector fields, the potentials of the Kaluza-Klein (KK) modes in the corresponding Schr\"odinger equations are modified P\"oschl-Teller potentials, which lead to the localization of the scalar and vector zero modes on the brane as well as to mass gaps in the mass spectra. We also compute the corrections to Coulomb's law coming from massive KK vector modes. For spin-$1/2$ fermions, we introduce the bulk mass term $MF(z)\overline{\ensuremath{\Psi}}\ensuremath{\Psi}$ in the action, and four different cases are investigated. Localization of the massless left-chiral fermion zero mode is feasible for just two cases of $F(z)$. In the first one, we obtain Schr\"odinger equations with modified P\"oschl-Teller potentials with the corresponding mass gaps for both left- and right-chiral fermions; the number of massive KK bound states is finite (determined by the ratio $M/b$) and is the same for left- and right-chiral modes. In the second case, we get a family of solutions with an infinite number of bound states where the mass spectra for left- and right-chiral KK fermion modes are discrete. A special case resembles the one-dimensional quantum harmonic oscillator problem. For both of these cases, the mass spectrum of right-chiral fermions is shifted with respect to the mass spectrum of the left-chiral ones.

Non-Fefferman-Graham asymptotics and holographic renormalization in new massive gravity

The asymptotic behavior of new massive gravity (NMG) is analyzed for all values of the mass parameter satisfying the Breitenlohner-Freedman bound. The traditional Fefferman-Graham expansion fails to capture the dynamics of NMG, and new terms in the asymptotic expansion are needed to include the massive graviton modes. New boundary conditions are discovered for a range of values $-1<2m^2l^2<1$ at which non-Einstein modes decay more slowly than the Brown-Henneaux boundary conditions. The holographically renormalized stress tensor is computed for these modes, and the relevant counterterms are identified up to unphysical ambiguities.