Massless Modes Research Articles

Antisymmetric tensor propagator with spontaneous Lorentz violation

In this work, we study the spontaneous Lorentz symmetry breaking due to an antisymmetric 2-tensor field in Minkowski spacetime. For a smooth quadratic potential, the spectrum of the theory exhibits massless and massive excitations. We show that the equations of motion for the free field obey some constraints which lead to the massive mode being nonpropagating at leading order. Besides, there exists a massless mode in the theory which can be identified with the usual Kalb-Ramond field, carrying only one on-shell degree of freedom. The same conclusion holds when one analyses the pole structure of its Feynman propagator. A new complete set of spin-type operators is found, which was the requirement to evaluate the propagator of the Kalb-Ramond field modified by the presence of a nonzero vacuum expectation value responsible for the Lorentz violation.

Higher order clockwork gravity

We present a higher order generalisation of the clockwork mechanism starting from an underlying non-linear multigravity theory with a single scale and nearest neighbour ghost-free interactions. Without introducing any hierarchies in the underlying potential, this admits a family of Minkowski vacua around which massless graviton fluctuations couple to matter exponentially more weakly than the heavy modes. Although multi-diffeomorphisms are broken to the diagonal subgroup in our theory, an asymmetric distribution of conformal factors in the background vacua translates this diagonal symmetry into an asymmetric shift of the graviton gears. In particular we present a TeV scale multigravity model with ${\cal O}(10)$ sites that contains a massless mode whose coupling to matter is Planckian, and a tower of massive modes starting at a TeV mass range and with TeV strength couplings. This suggests a possible application to the hierarchy problem as well as a candidate for dark matter.

Invisibility of antisymmetric tensor fields in the light of F(R) gravity

A natural question arises from observable signatures of scalar, fermion, and vector degrees of freedom (d.o.f.) in our Universe along with spin 2 symmetric tensor field in the form of gravity: why is our Universe is free of any perceptible signature of massless antisymmetric tensor modes? This work brings out a natural explanation of these phenomena through higher curvature quantum d.o.f. in the gravity sector that were dominant in the early universe. In the backdrop of a F(R) gravity model, we propose how the scalar d.o.f. associated with higher curvature term in the model can generate a heavily suppressed coupling between any antisymmetric massless modes and various standard model fields.

Massless and quantized modes of kinks in the phase space of superconducting gaps

We investigated quantized modes of kinks in the phase space of superconducting gaps in a superconductor with multiple gaps. The kink is described by the sine-Gordon model in a two-gap superconductor and by the double sine-Gordon model in a three-gap superconductor. A fractional-flux vortex exists at the edge of the kink, and a fractional-flux vortex will be stable in a three-gap superconductor with time-reversal symmetry breaking. The kink and fractional-flux vortex exhibit massless modes as a sliding motion. We show further that there are one zero-energy mode (massless mode) and quantized excitation modes in kinks, which are characteristic features of multi-gap superconductors. The equation of quantized modes for the double sine-Gordon model is solved numerically. The correction to the ground-state energy is calculated based on the renormalization theory.

Astrophysical gravitational waves in conformal gravity

We investigate the gravitational radiation from binary systems in conformal gravity (CG) and massive conformal gravity (MCG). CG might explain observed galaxy rotation curves without dark matter, and both models are of interest in the context of quantum gravity. Here we show that gravitational radiation emitted by compact binaries allows us to strongly constrain both models. We work in Weyl gauge, which fixes the rescaling invariance of the models, and derive the linearized fourth-order equation of motion for the metric, which describes massless and massive modes of propagation. In the limit of a large graviton mass, MCG reduces to general relativity (GR), whereas CG does not. Coordinates are fixed by Teyssandier gauge to show that for a conserved energy-momentum tensor the gravitational radiation is due to the time-dependent quadrupole moment of a non-relativistic source and we derive the gravitational energy-momentum tensor for both models. We apply our findings to the case of close binaries on circular orbits, which have been used to indirectly infer the existence of gravitational radiation prior to the direct observation of gravitational waves. As an example, we analyze the binary system PSR J1012+5307, chosen for its small eccentricity. When fixing the graviton mass in CG such that observed galaxy rotation curves could be explained without dark matter, the gravitational radiation of a binary system is much smaller than in GR. The same holds for MCG for small masses of the graviton. Thus gravitational radiation cannot explain the orbital decay of binary systems and replace dark matter simultaneously. We also analyse MCG for large graviton masses and conclude that MCG can describe the orbital periods of compact binaries in agreement with data, as it reduces to GR in that limit.

The low-energy limit of AdS3/CFT2 and its TBA

We investigate low-energy string excitations in AdS3 × S3 × T4. When the worldsheet is decompactified, the theory has gapless modes whose spectrum at low energies is determined by massless relativistic integrable S matrices of the type introduced by Al. B. Zamolodchikov. The S matrices are non-trivial only for excitations with identical worldsheet chirality, indicating that the low-energy theory is a CFT2. We construct a Thermodynamic Bethe Ansatz (TBA) for these excitations and show how the massless modes’ wrapping effects may be incorporated into the AdS3 spectral problem. Using the TBA and its associated Y-system, we determine the central charge of the low-energy CFT2 to be c = 6 from calculating the vacuum energy for antiperiodic fermions — with the vacuum energy being zero for periodic fermions in agreement with a supersymmetric theory — and find the energies of some excited states.

RG flows and cascades of Lif4(2)\u2009\xd7\u2009S1\u2009\xd7\u2009S5 vacua

The (F1,D2,D8) brane configuration produces Lif4(2) × S1 × S5 Lifshitz vacua supported by ‘massive’ B-field. We present exact deformations of this system under which new massless B-modes of strings also get excited. Due to these massless modes the deformed solutions flow to conformally Lif4(3) × S1 × S5 vacua in the IR. The latter types are supersymmetric solutions of ordinary type IIA theory. The massive and massless Bμν modes segregate out in the IR. We confirm that the massive B mode and cosmological constant indeed decouple from the theory rendering the IR field dynamics controlled by massless fields only. A similar effect is observed on the UV side of the flow where a relativistic regime reappears. We also present ‘cascading’ Lifshitz vacua in which dynamical exponent has integral jumps along the flow; Lif4(3) → Lif4(2) → Lif4(1). The critical Lif4(2) theory separates ‘deconfining’ Lif4(3) IR theory from the confining Yang-Mills phase in UV.

Chiral lattice supersolid on edges of quantum spin Hall samples

We show that edges of Quantum Spin Hall topological insulators represent a natural platform for realization of exotic supersolid phase. On one hand, fermionic edge modes are helical due to the nontrivial topology of the bulk. On the other hand, a disorder at the edge or magnetic adatoms may produce a dense array of localized spins interacting with the helical electrons. The spin subsystem is magnetically frustrated since the indirect exchange favors formation of helical spin order and the direct one favors (anti)ferromagnetic ordering of the spins. At a moderately strong direct exchange, the competition between these spin interactions results in the spontaneous breaking of parity and in the Ising type order of the $z$-components at zero temperature. If the total spin is conserved the spin order does not pin a collective massless helical mode which supports the ideal transport. In this case, the phase transition converts the helical spin order to the order of a chiral lattice supersolid. This represents a radically new possibility for experimental studies of the elusive supersolidity.

The role of long relaxation times in a simple model with massless modes

The next-nearest-neighbour Ising model with competing nearest-neighbour (nn) and next-nearest-neighbour (nnn) interactions, provides an example of a system in which massless modes destroy order at any finite temperature. This occurs only at a critical ratio, Kc, of the nnn and nn interactions. In this paper we investigate the role of long relaxation times in determining the behaviour of the system when the ratio of the nnn and nn interactions, K, is at and close to this critical ratio. Despite the absence of an order–disorder transition in systems with K = Kc, in Monte Carlo simulations reported here the temperature-dependent behaviour of the relaxation times indicates the existence of a glass transition with a glass transition temperature of Tg ≈ 0.26 in a model with nn interaction J = kB = 1.

Scalar enhancement of the photon electric field by the tail of the graviton propagator

One graviton loop corrections to the vacuum polarization on de Sitter show two interesting infrared effects: a secular enhancement of the photon electric field strength and a long range running of the Coulomb potential. We show that the first effect derives solely from the "tail" term of the graviton propagator, but that the second effect does not. Our result agrees with the earlier observation that the secular enhancement of massless fermion mode functions derives from solely from the tail term. We discuss the implications this has for the important project of generalizing to quantum gravity the Starobinsky technique for summing the series of leading infrared effects from inflationary quantum field theory.

Stable Palatini f(R) braneworld

We consider the static domain wall braneworld scenario constructed from the Palatini formalism $f(\mathcal{R})$ theory. We check the self-consistency under scalar perturbations. By using the scalar-tensor formalism we avoid dealing with the higher-order equations. We develop the techniques to deal with the coupled system. We show that under some conditions, the scalar perturbation simply oscillates with time, which guarantees the stability. We also discuss the localization condition of the scalar mode by analyzing the effective potential and the fifth dimensional profile of the scalar mode. We apply these results to an explicit example, and show that only some of the solutions allow for stable scalar perturbations. These stable solutions also give nonlocalizable massless mode. This is important for reproducing a viable four-dimensional gravity.

Geometrically induced broadening for phonon blocking at low temperatures

Because of the presence of robust massless modes with no excitation gap, the heat current carried by phonons tends to survive at low temperatures even when scattering mechanisms are incorporated into the system. This becomes a fundamental obstacle to thermoelectric applications at low temperatures. In this study, we investigate the effect of energy broadening on phonon transport in mesoscopic systems coupled to leads or probes in various geometries using a nonequilibrium Green's function formalism. An analytic theory derived from a minimal model consisting of a harmonic chain shows that geometrically induced broadening sizably suppresses low-temperature phonon transport. It is also demonstrated from numerical calculations that this scheme for phonon blocking is viable for realistic systems in higher dimensions.

Dynamical generation of fermion mass hierarchy in an extra dimension

We propose a new mechanism to produce a fermion mass hierarchy dynamically in a model with a singlet generation of fermions. A five dimensional gauge theory on an interval with point interactions (zero-width branes) takes responsibility for realizing three generations and each massless zero mode localizes at boundaries of the segments on the extra dimension. An extra-dimension coordinate-dependent vacuum expectation value of a scalar field makes large differences in overlap integrals of the localized zero modes and then an exponential fermion mass hierarchy can appear. The positions of the point interactions control the magnitude of the fermion mass hierarchy and are determined by the minimization condition of the Casimir energy. As a result of the minimization of the Casimir energy, an exponential mass hierarchy appears dynamically. We also discuss the stability of the extra dimension.

Localized non-Abelian gauge fields in non-compact extra dimensions

Dynamical localization of non-Abelian gauge fields in non-compact flat $D$ dimensions is worked out. The localization takes place via a field-dependent gauge kinetic term when a field condenses in a finite region of spacetime. Such a situation typically arises in the presence of topological solitons. We construct four-dimensional low-energy effective Lagrangian up to the quadratic order in a universal manner applicable to any spacetime dimensions. We devise an extension of the $R_\xi$ gauge to separate physical and unphysical modes clearly. Out of the D-dimensional non-Abelian gauge fields, the physical massless modes reside only in the four-dimensional components, whereas they are absent in the extra-dimensional components. The universality of non-Abelian gauge charges holds due to the unbroken four-dimensional gauge invariance. We illustrate our methods with models in $D=5$ (domain walls), in $D=6$ (vortices), and in $D=7$.

Signatures of extra dimensions in gravitational waves from black hole quasinormal modes

In this work we have derived the evolution equation for gravitational perturbation in four dimensional spacetime in presence of a spatial extra dimension. The evolution equation is derived by perturbing the \emph{effective} gravitational field equations on the four dimensional spacetime, which inherits non-trivial higher dimensional effects. Note that this is \emph{different} from the perturbation of the five dimensional gravitational field equations, existing in literature, and possess quantitatively new features. The gravitational perturbation has further been decomposed into a purely four dimensional part and another piece that depends on extra dimensions. The four dimensional gravitational perturbation now admits massive propagating degrees of freedom, owing to the existence of higher dimensions. We have also studied the influence of these massive propagating modes on the quasi-normal mode frequencies, signaling the higher dimensional nature of the spacetime, and have contrasted these massive modes with the massless modes in general relativity. Surprisingly, it turns out that the massive modes experience much smaller damping compared to the massless modes in general relativity and may even \emph{dominate} over and above the general relativity contribution if one observes the ringdown phase of a black hole merger event at sufficiently late times. Furthermore, the whole analytical framework has been supplemented by the fully numerical Cauchy evolution problem as well. In this context we have shown that except for minute details the overall features of the gravitational perturbations are captured in both the Cauchy evolution as well as in the analysis of quasi-normal modes. The implications on observations of black holes with LIGO and proposed space missions like LISA are also discussed.

The future of gravitational theories in the era of the gravitational wave astronomy

We discuss the future of gravitational theories in the framework of gravitational wave (GW) astronomy after the recent GW detections (the events GW150914, GW151226, GW170104, GW170814, GW170817 and GW170608). In particular, a calculation of the frequency and angular dependent response function that a GW detector would see if massive modes from [Formula: see text] theories or scalar–tensor gravity (STG) were present, allowing for sources incident from any direction on the sky, is shown. In addition, through separate theoretical results which do not involve the recent GW detections, we show that [Formula: see text] theories of gravity having a third massless mode are ultimately ruled out while there is still room for STG having a third (massive or massless) mode and for [Formula: see text] theories of gravity having a third massive mode.

Dark matter scenarios with multiple spin-2 fields

We study ghost-free multimetric theories for (N+1) tensor fields with a coupling to matter and maximal global symmetry group SN×(Z2)N. Their mass spectra contain a massless mode, the graviton, and N massive spin-2 modes. One of the massive modes is distinct by being the heaviest, the remaining (N−1) massive modes are simply identical copies of each other. All relevant physics can therefore be understood from the case N=2. Focussing on this case, we compute the full perturbative action up to cubic order and derive several features that hold to all orders in perturbation theory. The lighter massive mode does not couple to matter and neither of the massive modes decay into massless gravitons. We propose the lighter massive particle as a candidate for dark matter and investigate its phenomenology in the parameter region where the matter coupling is dominated by the massless graviton. The relic density of massive spin-2 can originate from a freeze-in mechanism or from gravitational particle production, giving rise to two different dark matter scenarios. The allowed parameter regions are very different from those in scenarios with only one massive spin-2 field and more accessible to experiments.

Fermion localization in higher curvature and scalar\u2013tensor theories of gravity

It is well known that, in a braneworld model, the localization of fermions on a lower dimensional submanifold (say a TeV 3-brane) is governed by the gravity in the bulk, which also determines the corresponding phenomenology on the brane. Here we consider a five dimensional warped spacetime where the bulk geometry is governed by higher curvature like F(R) gravity. In such a scenario, we explore the role of higher curvature terms on the localization of bulk fermions which in turn determines the effective radion–fermion coupling on the brane. Our result reveals that, for appropriate choices of the higher curvature parameter, the profiles of the massless chiral modes of the fermions may get localized near the TeV brane, while those for massive Kaluza–Klein (KK) fermions localize towards the Planck brane. We also explore these features in the dual scalar–tensor model by appropriate transformations. The localization property turns out to be identical in the two models. This rules out the possibility of any signature of massive KK fermions in TeV scale collider experiments due to higher curvature gravity effects.

4D higher spin black holes with nonlinear scalar fluctuations

We construct an infinite-dimensional space of solutions to Vasiliev’s equations in four dimensions that are asymptotic to AdS spacetime and superpose massless scalar particle modes over static higher spin black holes. Each solution is obtained by a large gauge transformation of an all-order perturbatively defined particular solution given in a simple gauge, in which the spacetime connection vanishes, the twistor space connection is holomorphic, and all local degrees of freedom are encoded into the residual twistor space dependence of the spacetime zero-forms. The latter are expanded over two dual spaces of Fock space operators, corresponding to scalar particle and static black hole modes, equipped with positive definite sesquilinear and bilinear forms, respectively. Switching on an AdS vacuum gauge function, the twistor space connection becomes analytic at generic spacetime points, which makes it possible to reach Vasiliev’s gauge, in which Fronsdal fields arise asymptotically, by another large transformation given here at first order. The particle and black hole modes are related by a twistor space Fourier transform, resulting in a black hole backreaction already at the second order of classical perturbation theory. We speculate on the existence of a fine-tuned branch of moduli space that is free from black hole modes and directly related to the quasi-local deformed Fronsdal theory. Finally, we comment on a possible interpretation of the higher spin black hole solutions as black-hole microstates.

Covariant variational approach to Yang-Mills theory: Thermodynamics

The thermodynamics of $SU(2)$ Yang-Mills theory in the covariant variational approach is studied by relating the free action density in the background of a non-trivial Polyakov loop to the pressure of the gluon plasma. The correct subtraction of the vacuum contribution in the free action density is argued for. The Poisson resummed expression for the pressure can be evaluated analytically in limiting cases, and shows the correct Stefan-Boltzmann limit at $T \to \infty$, while the limit $T \to 0$ is afflicted by artifacts due to massless modes in the confined phase. Several remedies to remove these artifacts are discussed. Using the numerical $T=0$ solutions for the ghost and gluon propagators in the covariant variational approach as input, the pressure, energy density and interaction strength are calculated and compared to lattice data.