Massive Modes Research Articles

Polarization states of gravitational waves in modified theories

In this paper, we present polarization states of gravitational waves in modified theories. Particularly, we consider scalar–tensor theory and evaluate the extra polarization modes which appear other than the theory of general relativity. It is found that these metric theories present two extra states of polarization, the breathing massless transverse and massive longitudinal mode in the direction of propagation.

Exotic Elko on string-like defects in six dimensions

We analyse the trapping of eigenspinors of the charge conjugation operator with dual helicity (Elko), in thin and thick string-like models with codimension-2. Elko spinor fields describe mass-dimension-one fermions in four dimensions (and, correspondingly, mass-dimension-two fermions in six dimensions), that represent natural dark-matter prime candidates. This dark spinor has many applications, from particle physics to cosmology. On the other hand, six-dimensional brane-world models have, among other prominent features, the spontaneous confinement of free spin-1 fields and a mechanism that explains the mass hierarchy of fundamental fermions. In this paper, we use scalar couplings in order to confine the zero mode of Elko in six dimensions. Moreover, we use the Elko dark-spinor features to propose an exotic coupling in order to remove the complex-valued terms in the massive Kaluza-Klein modes. Hence, we show that six-dimensional models can resolve the main issues of Elko fields confinement presented in five dimensions.

Dirac equation for spherically symmetric AdS5 spacetime and application to a boson star in EGB gravity

We discuss the Dirac equation in a curved 5-dimensional spherically symmetric spacetime. The angular part of the solutions is thoroughly studied, in a formulation suited for extending to rotating spacetimes with equal angular momenta. It has a symmetry [Formula: see text] and is implemented by the Wigner functions. The radial part forms a Dirac–Schrödinger type equation, and existence of the analytical solutions of the massless and the massive modes is confirmed. The solutions are described by the Jacobi polynomials. Also, the spinor of the both large and small components is obtained numerically. As a direct application of our formulation, we evaluate the spectrum of the Dirac fermion in Einstein–Gauss–Bonnet spacetime and the spacetime of a boson star.

Yang-Mills glueballs as closed bosonic strings

We put forward the Axionic String Ansatz (ASA), which provides a unified description for the worldsheet dynamics of confining strings in pure Yang-Mills theory both in D = 3 and D = 4 space-time dimensions. The ASA is motivated by the excitation spectrum of long confining strings, as measured on a lattice, and by recently constructed integrable axionic non-critical string models. According to the ASA, pure gluodynamics in 3D is described by a non-critical bosonic string theory without any extra local worldsheet degrees of freedom. We argue that this assumption fixes the set of quantum numbers (spins, P-and C-parities) of almost all glueball states. We confront the resulting predictions with the properties of approximately 12 + 22 + 32 + 52 = 39 lightest glueball states measured on a lattice and find a good agreement. On the other hand, the spectrum of low lying glueballs in 4D gluodynamics suggests the presence of a massive pseudoscalar mode on the string worldsheet, in agreement with the ASA and lattice data for long strings.

Kaluza-Klein reduction of massive and partially massless spin-2 fields

We describe the dimensional reduction of massive and partially massless spin-2 fields on general Einstein direct product manifolds. As with massless fields, the higher-dimensional gauge symmetry of the partially massless field displays itself upon dimensional reduction as a tower of St\"uckelberg symmetries for the massive modes of the tower. Unlike the massless case, the zero mode of the gauge symmetry does not display itself as a lower-dimensional non-Stuckelberg gauge symmetry enforcing partial masslessness on the zero mode. Partial masslessness is destroyed by the dimensional reduction and the zero mode gauge symmetry instead serves to eliminate the radion. In addition, we study the fully non-linear dimensional reduction of dRGT massive gravity on a circle, which results in a massive scalar-tensor-vector theory which we expect to be ghost-free, and whose scalar-tensor sector is a special case of mass-varying massive gravity.

On the cancellation of Newtonian singularities in higher-derivative gravity

Recently there has been a growing interest in quantum gravity theories with more than four derivatives, including both their quantum and classical aspects. In this work we extend the recent results concerning the non-singularity of the modified Newtonian potential to the most relevant case in which the propagator has complex poles. The model we consider is Einstein-Hilbert action augmented by curvature-squared higher-derivative terms which contain polynomials on the d'Alembert operator. We show that the classical potential of these theories is a real quantity and it is regular at the origin disregard the (complex or real) nature or the multiplicity of the massive poles. The expression for the potential is explicitly derived for some interesting particular cases. Finally, the issue of the mechanism behind the cancellation of the singularity is discussed; specifically we argue that the regularity of the potential can hold even if the number of massive tensor modes and scalar ones is not the same.

Extended vector-tensor theories

Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.

Strongly correlated Fermi superfluid near an orbital Feshbach resonance: Stability, equation of state, and Leggett mode

We theoretically study the superfluid phase of a strongly correlated $^{173}$Yb Fermi gas near its orbital Feshbach resonance, by developing a quantitative pair-fluctuation theory within a two-band model. We examine the density excitation spectrum of the system and determine a stability phase diagram. We find that the $^{173}$Yb Fermi gas is intrinsically metastable and has a peculiar equation of state, due to the small but positive singlet scattering length. The massive Leggett mode, arising from the fluctuation of the relative phase of two order parameters, is severely damped. We discuss the parameter space where an undamped Leggett mode may exist.

Multiresonance modes in sine–Gordon brane models

In this work, we study the localization of the vector gauge field in two five-dimensional braneworlds generated by scalar fields coupled to gravity. The sine–Gordon like potentials are employed to produce different thick brane setups. A zero mode localized is obtained, and we show the existence of reverberations with the wave solutions indicating a quasi-localized massive mode. More interesting results are achieved when we propose a double sine–Gordon potential to the scalar field. The resulting thick brane shows a more detailed topology with the presence of an internal structure composed by two kinks. The massive spectrum of the gauge field is revalued on this scenario revealing the existence of various resonant modes. Furthermore, we compute the corrections to Coulomb law coming from these massive KK vector modes in these thick scenarios, which is concluded that the dilaton parameter regulates these corrections.

Closed flux tubes in D = 2 + 1 SU(N ) gauge theories: dynamics and effective string description

We extend our earlier calculations of the spectrum of closed flux tubes in SU(N) gauge theories in 2+1 dimensions, with a focus on questions raised by recent theoretical progress on the effective string action of long flux tubes and the world-sheet action for flux tubes of moderate lengths. Our new calculations in SU(4) and SU(8) provide evidence that the leading O(1/l^gamma) non-universal correction to the flux tube ground state energy does indeed have a power gamma greater than or equal to 7. We perform a study in SU(2), where we can traverse the length at which the Nambu-Goto ground state becomes tachyonic, to obtain an all-N view of the spectrum. Our comparison of the k=2 flux tube excitation energies in SU(4) and SU(6) suggests that the massive world sheet excitation associated with the k=2 binding has a scale that knows about the group and hence the theory in the bulk, and we comment on the potential implications of world sheet massive modes for the bulk spectrum. We provide a quantitative analysis of the surprising (near-)orthogonality of flux tubes carrying flux in different SU(N) representations, which implies that their screening by gluons is highly suppressed even at small N.

Topological massive Dirac edge modes and long-range superconducting Hamiltonians

We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display symmetry-protected topological order measured by the Berry/Zak phase of the lower band eigenvector and the winding number of the Hamiltonians. For exponentially-decaying hopping amplitudes, the topological sector can be significantly augmented as the penetration length increases, something experimentally achievable. For power-law decaying superconducting pairings, the massless Majorana modes at the edges get paired together into a massive non-local Dirac fermion localised at both edges of the chain: a new topological quasiparticle that we call topological massive Dirac fermion. This topological phase has fractional topological numbers as a consequence of the long-range couplings. Possible applications to current experimental setups and topological quantum computation are also discussed.

Adiabatic quenches and characterization of amplitude excitations in a continuous quantum phase transition

Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu-Goldstone modes and massive Anderson-Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble-Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition.

On the curious spectrum of duality invariant higher-derivative gravity

We analyze the spectrum of the exactly duality and gauge invariant higher-derivative double field theory. While this theory is based on a chiral CFT and does not correspond to a standard string theory, our analysis illuminates a number of issues central in string theory. The full quadratic action is rewritten as a two-derivative theory with additional fields. This allows for a simple analysis of the spectrum, which contains two massive spin-2 ghosts and massive scalars, in addition to the massless fields. Moreover, in this formulation, the massless or tensionless limit $\alpha'\rightarrow \infty$ is non-singular and leads to an enhanced gauge symmetry. We show that the massive modes can be integrated out exactly at the quadratic level, leading to an infinite series of higher-derivative corrections. Finally, we present a ghost-free massive extension of linearized double field theory, which employs a novel mass term for the dilaton and metric.

Complex-mass shell renormalization of the higher-derivative electrodynamics

We consider a higher-derivative extension of QED modified by the addition of a gauge-invariant dimension-6 kinetic operator in the U(1) gauge sector. The Feynman diagrams at one-loop level are then computed. The modification in the spin-1 sector leads the electron self-energy and vertex corrections diagrams finite in the ultraviolet regime. Indeed, no regularization prescription is used to calculate these diagrams because the modified propagator always occurs coupled to conserved currents. Moreover, besides the usual massless pole in the spin-1 sector, there is the emergence of a massive one, which becomes complex when computing the radiative corrections at one-loop order. This imaginary part defines the finite decay width of the massive mode. To check consistency, we also derive the decay length using the electron--positron elastic scattering and show that both results are equivalent. Because the presence of this unstable mode, the standard renormalization procedures cannot be used and is necessary adopt an appropriate framework to perform the perturbative renormalization. For this purpose, we apply the complex-mass shell scheme (CMS) to renormalize the aforementioned model. As an application of the formalism developed, we estimate a quantum bound on the massive parameter using the measurement of the electron anomalous magnetic moment and compute the Uehling potential. At the end, the renormalization group is analyzed.

De Sitter thin brane model

We discuss the large mass hierarchy problem in a braneworld model which represents our acceleratively expanding universe. The Randall-Sundrum (RS) model with warped one extra dimension added to flat 4-dimensional space-time cannot describe our expanding universe. Here, we study instead the de Sitter thin brane model. This is described by the same action as that for the RS model, but the 4-dimensional space-time on the branes is $\rm dS_4$. We study the model for both the cases of positive 5-dimensional cosmological constant $\Lambda_5$ and negative one. In the positive $\Lambda_5$ case, the 4-dimensional large hierarchy necessitates a 5-dimensional large hierarchy, and we cannot get a natural explanation. On the other hand, in the negative $\Lambda_5$ case, the large hierarchy is naturally realized in the 5-dimensional theory in the same manner as in the RS model. Moreover, another large hierarchy between the Hubble parameter and the Planck scale is realized by the ${\mathcal O}(10^2)$ hierarchy of the 5-dimensional quantities. Finally, we find that the lightest mass of the massive Kaluza-Klein modes and the intervals of the mass spectrum are of order $10^2\,\rm GeV$, which are the same as in the RS case and do not depend on the value of the Hubble parameter.

Gravitational wave polarization modes inf(R)theories

Many studies have been carried out in the literature to evaluate the number of polarization modes of gravitational waves in modified theories, in particular in $f(R)$ theories. In the latter ones, besides the usual two transverse-traceless tensor modes present in general relativity, there are two additional scalar ones: a massive longitudinal mode and a massless transverse mode (the so-called breathing mode). This last mode has often been overlooked in the literature, due to the assumption that the application of the Lorenz gauge implies transverse-traceless wave solutions. We however show that this is in general not possible and, in particular, that the traceless condition cannot be imposed due to the fact that we no longer have a Minkowski background metric. Our findings are in agreement with the results found using the Newman-Penrose formalism, and thus clarify the inconsistencies found so far in the literature.

Pure geometric thick f(R)-branes: stability and localization of gravity

We study two exactly solvable five-dimensional thick brane world models in pure metric $f(R)$ gravity. Working in the Einstein frame, we show that these solutions are stable against small linear perturbations, including the tensor, vector, and scalar modes. For both models, the corresponding gravitational zero mode is localized on the brane, which leads to the four-dimensional Newton's law; while the massive modes are nonlocalized and only contribute a small correction to the Newton's law at a large distance.

Coulomb's law corrections and fermion field localization in a tachyonic de Sitter thick braneworld

Following recent studies which show that it is possible to localize gravity as well as scalar and gauge vector fields in a tachyonic de Sitter thick braneworld, we investigate the solution of the gauge hierarchy problem, the localization of fermion fields in this model, the recovering of the Coulomb law on the non-relativistic limit of the Yukawa interaction between bulk fermions and gauge bosons localized in the brane, and confront the predicted 5D corrections to the photon mass with its upper experimental/observational bounds, finding the model physically viable since it passes these tests. In order to achieve the latter aims we first consider the Yukawa interaction term between the fermionic and the tachyonic scalar fields MF(T)ΨΨ̅ in the action and analyze four distinct tachyonic functions F(T) that lead to four different structures of the respective fermionic mass spectra with different physics. In particular, localization of the massless left-chiral fermion zero mode is possible for three of these cases. We further analyze the phenomenology of these Yukawa interactions among fermion fields and gauge bosons localized on the brane and obtain the crucial and necessary information to compute the corrections to Coulomb's law coming from massive KK vector modes in the non-relativistic limit. These corrections are exponentially suppressed due to the presence of the mass gap in the mass spectrum of the bulk gauge vector field. From our results we conclude that corrections to Coulomb's law in the thin brane limit have the same form (up to a numerical factor) as far as the left-chiral massless fermion field is localized on the brane. Finally we compute the corrections to the Coulomb's law for an arbitrarily thick brane scenario which can be interpreted as 5D corrections to the photon mass. By performing consistent estimations with brane phenomenology, we found that the predicted corrections to the photon mass, which are well bounded by the experimentally observed or astrophysically inferred photon mass, are far beyond its upper bound, positively testing the viability of our tachyonic braneworld. Moreover, the 5D parameters that define these corrections possess the same order, providing naturalness to our model, however, a fine-tuning between them is needed in order to fit the corresponding upper bound on the photon mass.

Non-minimally coupled pseudoscalars in AdS4 for instantons in CFT3

For the 11-dimensional supergravity over , beginning with a general four-form ansatz and the main geometry unchanged, we get a tower of massive and tachyonic pseudoscalars. Indeed, the resultant equations can be assigned to the so-called actions of the non-minimally coupled scalar-tensor theories with a cosmological constant. We focus on a well-known tachyonic and a new massive bulk mode, which are singlet under the internal group and break all supersymmetries, associated with skew-whiffing and Wick-rotating of the background four-form flux, respectively. The first one is the conformally coupled pseudoscalar in the bulk of Euclidean AdS4, where an exact instanton solution is found and a marginally triple-trace deformation with a proper dimension-1 operator produces an agreeing boundary solution with finite action. From the action evaluated on the solution, we estimate the decay rate of the vacuum tunneling mediated by the instanton. Another massive mode, with the so-called non-minimal coupling parameter , also breaks the conformal invariance and so there is no exact solution. Then, based on the AdS4/CFT3 correspondence rules, we propose the dimension-4 () boundary operator in the skew-whiffed (anti-M2-branes) theory with which to deform the boundary action—consisting of a singlet fermion, an original scalar and U(1) gauges fields—and find some solutions to be matched with the bulk solutions.

Localization and mass spectrum of q -form fields on branes

In this paper, we investigate localization of a bulk massless q-form field on codimension-one brane by using a new Kaluza-Klein (KK) decomposition, for which there are two types of KK modes for the bulk q-form field, the q-form and (q-1)-form modes. The first modes may be massive or massless while the second ones are all masselss. These two types fo KK modes satisfy twy Schrodinger-like equations. For a five-dimensional brane model with a finite dimension, the spectrum of a bulk 3-form field on the brane consists of some massive bound 3-form KK modes as well as some massless bound 2-form ones with different configuration along the extra dimension. These 2-form modes are different form those obtained from a bulk 2-form field. For a five-dimensional degenerated Bloch brane model with an infinite extra dimension, some massive 3-form resonant KK modes and corresponding massless 2-form resonant ones are obtained for a bulk 3-form field.