Massive Modes Research Articles

Gravitational waves in modified Gauss–Bonnet gravity

We study the gravitational waves (GWs) in modified Gauss–Bonnet gravity. Applying the metric perturbation around a cosmological background, we obtain explicit expressions for the wave equations. It is shown that the speed of the traceless mode is equal to the speed of light. An additional massive scalar mode appears in the propagation of the GWs. To find phenomena beyond the general relativity, the scalar mode mass is calculated as a function of the background curvature in some typical models.

Consistent inflationary cosmology from quadratic gravity with dynamical torsion

The idea of gauge theories of gravity predicts that there should exist not only the massless graviton but also massive particles carrying the gravitational force. We study the cosmology in a quadratic gravity with dynamical torsion where gravity may be interpreted as a gauge force associated with the Poincaré group. In addition to the massless spin-2 graviton, the model contains four non-ghost massive particle species: a couple of spin-0, a spin-1 and a spin-2. Supposing the restoration of the local Weyl invariance in the UV limit and the parity invariance, we find the most general minisuperspace action describing a homogeneous and isotropic universe with a flat spatial geometry. We then transform the minisuperspace action to a quasi-Einstein frame in which the field space is a hyperboloid and the field potential is a combination of those of a Starobinsky-like inflation and a natural inflation. Remarkably, thanks to the multi-field dynamics, the Starobinsky-like inflationary trajectory can be realized even if the initial condition is away from the top of the Starobinsky-like potential. We also study linear tensor perturbations and find qualitatively different features than the Starobinsky inflation, spontaneous parity violation and mixing of the massless and massive spin-2 modes, which might reveal the underlying nature of gravity through inflationary observables.

Spontaneously broken 3d Hietarinta/Maxwell Chern\u2013Simons theory and minimal massive gravity

We show that minimal massive 3d gravity (MMG) of (Bergshoeff et al. in Class Quantum Grav 31:145008, 2014), as well as the topological massive gravity, are particular cases of a more general ‘minimal massive gravity’ theory (with a single massive propagating mode) arising upon spontaneous breaking of a local symmetry in a Chern–Simons gravity based on a Hietarinta or Maxwell algebra. Similar to the MMG case, the requirements that the propagating massive mode is neither tachyon nor ghost and that the central charges of an asymptotic algebra associated with a boundary CFT are positive, impose restrictions on the range of the parameters of the theory.

Stringy excited baryons in holographic quantum chromodynamics

Abstract We analyze excited baryon states using a holographic dual of quantum chromodynamics that is defined on the basis of an intersecting D4/D8-brane system. Studies of baryons in this model have been made by regarding them as a topological soliton of a gauge theory on a five-dimensional curved spacetime. However, this allows one to obtain only a certain class of baryons. We attempt to present a framework such that a whole set of excited baryons can be treated in a systematic way. This is achieved by employing the original idea of Witten, which states that a baryon is described by a system composed of $N_c$ open strings emanating from a baryon vertex. We argue that this system can be formulated by an Atiyah–Drinfeld–Hitchin–Manin-type matrix model of Hashimoto–Iizuka–Yi together with an infinite tower of the open string massive modes. Using this setup, we work out the spectra of excited baryons and compare them with the experimental data. In particular, we derive a formula for the nucleon Regge trajectory assuming that the excited nucleons lying on the trajectory are characterized by the excitation of a single open string attached on the baryon vertex.

Generalized geometrical coupling for vector field localization on thick brane in asymptotic anti–de Sitter spacetime

It is known that a five-dimensional free vector field ${A}_{M}$ cannot be localized on Randall-Sundrum (RS)-like thick branes---namely, the thick branes embedded in asymptotic anti--de Sitter spacetime. To localize a vector field on the RS-like thick brane, an extra coupling term should be introduced. We generalize the geometrical coupling mechanism by adding two mass terms ($\ensuremath{\alpha}R{g}^{MN}{A}_{M}{A}_{N}+\ensuremath{\beta}{R}^{MN}{A}_{M}{A}_{N}$) to the action. We decompose the fundamental vector field ${A}_{M}$ into three parts: transverse vector part ${\stackrel{^}{A}}_{\ensuremath{\mu}}$ and scalar parts $\ensuremath{\phi}$ and ${A}_{5}$. Then we find that the transverse vector part ${\stackrel{^}{A}}_{\ensuremath{\mu}}$ decouples from the scalar parts. To eliminate the tachyonic modes of ${\stackrel{^}{A}}_{\ensuremath{\mu}}$, the two coupling parameters $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ should satisfy a relation. Combining the restricted condition, we can get a combination parameter as $\ensuremath{\gamma}=\frac{3}{2}\ifmmode\pm\else\textpm\fi{}\sqrt{1+12\ensuremath{\alpha}}$. Only if $\ensuremath{\gamma}>1/2$ can the zero mode of ${\stackrel{^}{A}}_{\ensuremath{\mu}}$ be localized on the RS-like thick brane. We also investigate the resonant character of the vector part ${\stackrel{^}{A}}_{\ensuremath{\mu}}$ for a general RS-like thick brane with a warp factor $A(z)=\ensuremath{-}\mathrm{ln}(1+{k}^{2}{z}^{2})/2$ by choosing the relative probability method. The results show that the massive resonant Kaluza-Klein modes can exist only for $\ensuremath{\gamma}>3$. The number of resonant Kaluza-Klein states increases with the combination parameter $\ensuremath{\gamma}$, and the lifetime of the first resonant state can be as long as our Universe's. This indicates that the vector resonances might be considered one of the candidates of dark matter. Combining the conditions of experimental observations, the constraint shows that the parameter $k$ has a lower limit with $k\ensuremath{\gtrsim}{10}^{\ensuremath{-}17}\text{ }\text{ }\mathrm{eV}$, the combination parameter $\ensuremath{\gamma}$ should be greater than 57, and, accordingly, the mass of the first resonant state should satisfy ${m}_{1}\ensuremath{\gtrsim}{10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{eV}$.

Power-counting renormalizable, ghost-and-tachyon-free Poincaré gauge theories

We present 48 further examples, in addition to the 10 identified in [1], of ghost-and-tachyon-free critical cases of parity-conserving Poincar\'e gauge theories of gravity (PGT$^+$) that are also power-counting renormalizable (PCR). This is achieved by extending the range of critical cases considered. Of the new PCR theories, seven have 2 massless degrees of freedom (d.o.f.) in propagating modes and a massive $0^-$ or $2^-$ mode, eight have only 2 massless d.o.f., and 33 have only massive mode(s). We also clarify the treatment of nonpropagating modes in determining whether a theory is PCR.

Fermion and graviton in Dirac\u2013Born\u2013Infeld braneworld models

In this paper, we study the braneworld models with non-standard kinetic term of Dirac–Born–Infeld (DBI) type in two case which are (I) in usual gravity and (II) in f(T) gravity. In each of these cases, we examine gravity localization on branes and show that both models are stable and capable of gravity localizing in a similar manner to the standard case of braneworld models. In addition, we investigate the problem of fermion localization in both models and by considering the Yukawa coupling as a function of the warp factor, we show that the massless zero mode of fermion fields are localized on both types of the the branes. Meanwhile, the effect of parameters in both models is addressed on the zero mode and massive mode of graviton and fermion and the effective potentials. Finally, we study the gauge hierarchy problem in both models and we show that by choosing the appropriate parameters, both models are able to solve the gauge hierarchy problem between the Tev scale and the Planck scale.

Nonminimal scalar-tensor theories

We compute the spectrum of scalar models with a general coupling to the scalar curvature. We find that the perturbative states of these theories are given by two massive spin-0 modes in addition to one massless spin-2 state. This latter mode can be identified with the standard graviton field. Indeed, we are able to define an Einstein frame, where the dynamics of the massless spin-2 graviton is the one associated with the Einstein-Hilbert action. We also explore the interactions of all these degrees of freedom in the mentioned frame, since part of the coupling structure can be anticipated by geometrical arguments.

Weak field limit and gravitational waves in f(T,\xa0B) teleparallel gravity

We derive the gravitational waves for fleft( T, Bright) gravity which is an extension of teleparallel gravity and demonstrate that it is equivalent to f(R) gravity by linearized the field equations in the weak field limit approximation. f(T, B) gravity shows three polarizations: the two standard of general relativity, plus and cross, which are purely transverse with two-helicity, massless tensor polarization modes, and an additional massive scalar mode with zero-helicity. The last one is a mix of longitudinal and transverse breathing scalar polarization modes. The boundary term B excites the extra scalar polarization and the mass of scalar field breaks the symmetry of the TT gauge by adding a new degree of freedom, namely a single mixed scalar polarization.

Quantum corrections to minimal surfaces with mixed three-form flux

We obtain the ratio of semiclassical partition functions for the extension under mixed flux of the minimal surfaces subtending a circumference and a line in Euclidean $AdS_{3}\times S^{3}\times T^{4}$. We reduce the problem to the computation of a set of functional determinants. If the Ramond-Ramond flux does not vanish, we find that the contribution of the $B$-field is comprised in the conformal anomaly. In this case, we successively apply the Gel'fand-Yaglom method and the Abel-Plana formula to the flat-measure determinants. To cancel the resultant infrared divergences, we shift the regularization of the sum over half-integers depending on whether it corresponds to massive or massless fermionic modes. We show that the result is compatible with the zeta-function regularization approach. In the limit of pure Neveu-Schwarz-Neveu-Schwarz flux we argue that the computation trivializes. We extend the reasoning to other surfaces with the same behavior in this regime.

Accelerated γ-face-centered cubic to ε-hexagonal close packed massive transformation in a laser powder bed fusion additively manufactured Co-29Cr-5Mo alloy

The γ-FCC (face-centered cubic) to ε-HCP (hexagonal close packed) phase transformation in a laser additively fabricated Co-29Cr-5Mo alloy was investigated. The microstructure of the as-built material was γ-FCC featured with a sub-micron scale dislocation cell structure and stacking faults. Aging at 1073 K led to rapid transformation within 0.5 h to the ε-HCP structure in a massive mode, characterized by: (i) composition invariance, (ii) oriented grain face nucleation; and (iii) interface-controlled linear growth mechanism. Effective lowering of the carbon content in the γ-FCC by partial tie-up as carbides along prior grain and dislocation cell boundaries and the diverse grain structure and interfaces are believed to promote the massive transformation.

Scale invariant gravity and black hole ringdown

Scale invariant theories of gravity give a compelling explanation to the early and late time acceleration of the Universe. Unlike most scalar-tensor theories, fifth forces are absent and it would therefore seem impossible to distinguish scale invariant gravity from general relativity. We show that the ringdown of a Schwarschild-de Sitter black hole may have a set of massive modes which are characteristic of scale invariant gravity. In principle these new modes can be used to distinguish scale invariant gravity from general relativity. In practice, we discuss the obstacles to generating these new massive modes and their detectability with future gravitational wave experiments but also speculate on their role in Kerr black holes.

Dynamics of revolving D-branes at short distances

We study the behavior of the effective potential between revolving Dp-branes at all ranges of the distance r, interpolating r » ls and r « ls (ls is the string length). Since the one-loop open string amplitude cannot be calculated exactly, we instead employ an efficient method of partial modular transformation. The method is to perform the modular transformation partially in the moduli parameter and rewrite the amplitude into a sum of contributions from both of the open and closed string massless modes. It is nevertheless free from the double counting and can approximate the open string amplitudes with less than 3% accuracy. From the D-brane effective field theory point of view, this amounts to calculating the one-loop threshold corrections of infinitely many open string massive modes. We show that threshold corrections to the ω2r2 term of the moduli field r cancel among them, where ω is the angular frequency of the revolution and sets the scale of supersymmetry breaking. This cancellation suggests a possibility to solve the hierarchy problem of the Higgs mass in high scale supersymmetry breaking models.

Thick brane in reduced Horndeski theory

Horndeski theory is the most general scalar-tensor theory retaining second-order field equations, although the action includes higher-order terms. This is achieved by a special choice of coupling constants. In this paper, we investigate the thick brane system in reduced Horndeski theory, especially the effects of the nonminimal derivative coupling and the cubic Galileon term on thick brane. First, the equations of motion are presented and a set of analytic background solutions are obtained. Then, the effects of these two terms on the thick brane are analyzed. It is found that the background solutions become asymmetric with the presence of the cubic Galileon term. However, the energy density of the thick brane is still symmetric with or without this term and splits with the presence of the nonminimal derivative coupling. The stability of the thick brane under tensor perturbation is also considered. It is shown that the tachyon is absent and the graviton zero mode can be localized on the brane. The localized graviton zero mode recovers the four-dimensional Newtonian potential and the presence of the nonminimal derivative coupling results in a splitting of its wave function. Besides, the presence of the cubic Galileon term results in the asymmetry of the effective potential and zero mode of the graviton. The correction of the massive graviton Kaluza-Klein modes to the Newtonian potential is also analyzed briefly.

Self-gravitating SU(5) Higgs domain walls as a braneworld

Five-dimensional domain walls in gauged $SU(5)$ generate a position-dependent symmetry breaking pattern along the additional dimension. We analyze the perturbative stability and the four-dimensional (4D) spectrum of these walls in the self-gravitating case, in terms of diffeomorphism-invariant and Lie algebra gauge-invariant field fluctuations. We show that tachyonic modes are absent, ensuring perturbative stability. As expected, gravitational tensor and vector fluctuations behave like their counterparts in the standard ${Z}_{2}$ domain walls. All the Lie algebra valued fluctuations exhibit towers of 4D massive modes, which propagate in the bulk, with a continuous spectrum starting from zero. All the would-be 4D Nambu-Goldstone fields, which are gravitationally trapped in the case of a global symmetry, are nontrivially absent. However, we find no localizable 4D gauge bosons, either massless or massive. Instead, quasilocalizable discrete 4D massive modes for the gauge field fluctuations are found, along the spontaneously broken directions.

Fermions localization on de Sitter branes

Spin 1/2 fields localization on an asymmetric dS${}_4$ scenario, where the brane interpolates between two spacetimes dS${}_5$ and AdS${}_5$, is determined. The bulk spinor is coupled to scalar field of the brane by a nonminimal Yukawa term compatible with the scenario's geometry. We show that, independently of wall's thickness, only one massless chiral mode is localized on the wall. The massive chiral modes follow a Schr\"odinger equation, whose potential has a mass gap determined by Yukawa constant, which is a generic property of this system. The fermions spectrum is defined bellow the gap, by bound states of both chiralities with the same mass, and above the gap, by a continuous spectrum with local and global resonant modes of both chiralities and different mass.

Spin-2 fields and the weak gravity conjecture

Recently, it has been argued that application of the Weak Gravity Conjecture (WGC) to spin-2 fields implies a universal upper bound on the cutoff of the effective theory for a single spin-2 field. We point out here that these arguments are largely spurious, because of the absence of states carrying spin-2 Stuckelberg $U(1)$ charge, and because of incorrect scaling assumptions. Known examples such as Kaluza-Klein theory that respect the usual WGC do so because of the existence of a genuine $U(1)$ field under which states are charged, as in the case of the Stuckelberg formulation of spin-1 theories, for which there is an unambiguously defined $U(1)$ charge. Theories of bigravity naturally satisfy a naive formulation of the WGC, $M_W< M_{\rm Pl}$, since the force of the massless graviton is always weaker than the massive spin-2 modes. It also follows that theories of massive gravity trivially satisfies this form of the WGC. We also point out that the identification of a massive spin-2 state in a truncated higher derivative theory, such as Einstein-Weyl-squared or its supergravity extension, bears no relationship with massive spin-2 states in the UV completion, contrary to previous statements in the literature. We also discuss the conjecture from a swampland perspective and show how the emergence of a universal upper bound on the cutoff relies on strong assumptions on the scale of the couplings between the spin-2 and other fields, an assumption which is known to be violated in explicit examples.

Scalar modes and the linearized Schwarzschild solution on a quantized FLRW space-time in Yang–Mills matrix models

We study scalar perturbations of a recently found 3+1-dimensional FLRW quantum space-time solution in Yang–Mills matrix models. In particular, the linearized Schwarzschild metric is obtained as a solution. It arises from a quasi-static would-be massive graviton mode, and slowly decreases during the cosmic expansion. Along with the propagating graviton modes, this strongly suggests that 3+1 dimensional (quantum) gravity emerges from the IKKT matrix model on this background. For the dynamical scalar modes, non-linear effects must be taken into account. We argue that they lead to non-Ricci-flat metric perturbations with very long wavelengths, which would be perceived as dark matter from the GR point of view.

Unitary Extension of Exotic Massive 3D Gravity from Bigravity.

We obtain a new 3D gravity model from two copies of parity-odd Einstein-Cartan theories. Using Hamiltonian analysis, we demonstrate that the only local degrees of freedom are two massive spin-2 modes. Unitarity of the model in anti-deSitter and Minkowski backgrounds can be satisfied for vast choices of the parameters without fine-tuning. The recent "exotic massive 3D gravity" model arises as a limiting case of the new model. We also show that there exist trajectories on the parameter space of the new model which cross the boundary between unitary and nonunitary regions. At the crossing point, one massive graviton decouples resulting in a unitary model with just one bulk degree of freedom but two positive central charges at odds with the usual expectation that the critical model has at least one vanishing central charge. Given the fact that a suitable nonrelativistic version of bigravity has been used as an effective theory for gapped spin-2 fractional quantum Hall states, our model may have interesting applications in condensed matter physics.

On the compositional partitioning during phase transformation in a binary ferromagnetic MnAl alloy

We introduce a new perspective on the classical massive mode of solid-state phase transformation enabled by the correlative use of atomic-scale electron microscopy and atom probe tomography. This is demonstrated in a binary MnAl alloy which has Heusler-like characteristics. In this system, the τ phase formed by a massive transformation from the high-temperature ε phase is metastable and ferromagnetic. The transformation results in a high density of micro-twins inside the newly grown τ phase. Atomic-scale compositional analysis across the interface boundaries and atomic structure of the micro-twins reveals the involvement of both structural modification and also the compositional partitioning during the growth of the τ phase. This is assisted by the migrating τ/ε interface boundary during transformation. Finally, the role of micro-twins on nucleating the equilibrium phases and the influence of the defects and phase formation on the magnetic properties are discussed.