Massless Spin Research Articles

On massive spin-3/2 in the Fradkin–Vasiliev formalism

One of the possible approaches to the construction of massive higher spin interactions is to use their gauge invariant description based on the introduction of the appropriate set of Stueckelberg fields. Recently, the general properties of such approach were investigated by Boulanger et al (2018 J. High Energy Phys. JHEP07(2018)021). The main findings of this work can be formulated in two statements. At first, there always exist enough field redefinitions to bring the vertex into abelian form where there are some corrections to the gauge transformations but the gauge algebra is undeformed. At second, with the further (as a rule higher derivative) field redefinitions one can bring the vertex into trivially gauge invariant form expressed in terms of the gauge invariant objects of the free theory. Our aim in this work is to show (using a simple example) how these general properties are realised in the so-called Fradkin–Vasiliev formalism and to see the effects (if any) that the presence of massless field, and hence of some unbroken gauge symmetries, can produce. As such example we take the gravitational interaction for massive spin-3/2 field so we complete the investigation started by Buchbinder et al (2014 Eur. Phys. J. C 74 3153) relaxing all restrictions on the number of derivatives and allowed field redefinitions. We show that in spite of the presence of massless spin-2 field, the first statement is still valid, while there exist two abelian vertices which are not equivalent on-shell to the trivially gauge invariant ones. Moreover, it is one of this abelian vertices that reproduce the minimal interaction for massive spin-3/2.

Analysis of the wave functions for accelerating Kerr-Newman metric

As is well-known, it is very difficult to solve wave equations in curved space-time. In this paper, we find that wave equations describing massless fields of the spins in accelerating Kerr-Newman black holes can be written as a compact master equation. The master equation can be separated to radial and angular equations, and both can be transformed to Heun’s equation, which shows that there are analytic solutions for all the wave equations of massless spin fields. The results not only demonstrate that it is possible to study the similarity between waves of gravitational and other massless spin fields, but also it can deal with other astrophysical applications, such as quasinormal modes, scattering, stability, etc. In addition, we also derive approximate solutions of the radial equation.

On Existence of Ground States in the Spin Boson Model

We show the existence of ground states in the massless spin boson model without any infrared regularization. Our proof is non-perturbative and relies on a compactness argument. It works for arbitrary values of the coupling constant under the hypothesis that the second derivative of the ground state energy as a function of a constant external magnetic field is bounded.

Kaluza-Klein from colour-kinematics duality for massive fields

We consider a broad class of massive four dimensional effective theories describing an infinite tower of charged massive spin 1 states, interacting with massless spin 1 and spin 0. The spectrum is chosen to be the same as that appears in the Kaluza-Klein theory reduction of 5d Yang-Mills to ensure the absence of any spurious poles in a possible double copy formulation. The effective theories are characterized by multiple different couplings between different fields which are unconstrained by symmetries and low energy criteria. Remarkably, by demanding that the scattering amplitudes preserve colour-kinematics duality for different scattering processes, required for the existence of a massive double copy, we find that our 4d Lagrangian is fixed uniquely to the Kaluza-Klein compactification of 5d Yang-Mills theory together with its known double copy consistent higher derivative operators.

Mathcal{N} = 2 supersymmetric partially massless fields and other exotic non-unitary superconformal representations

We find and classify the simplest mathcal{N} = 2 SUSY multiplets on AdS4 which contain partially massless fields. We do this by studying representations of the mathcal{N} = 2, d = 3 superconformal algebra of the boundary, including new shortening conditions that arise in the non-unitary regime. Unlike the mathcal{N} = 1 case, the simplest mathcal{N} = 2 multiplet containing a partially massless spin-2 is short, containing several exotic fields. More generally, we argue that mathcal{N} = 2 supersymmetry allows for short multiplets that contain partially massless spin-s particles of depth t = s − 2.

Remarks on Some Results Related to the Thermal Casimir Effect in Einstein and Closed Friedmann Universes with a Cosmic String

In this paper, we present a review of some recent results concerning the thermal corrections to the Casimir energy of massless scalar, electromagnetic, and massless spinor fields in the Einstein and closed Friedmann universes with a cosmic string. In the case of a massless scalar field, it is shown that the Casimir energy can be written as a simple sum of two terms; the first one corresponds to the Casimir energy for the massless scalar field in the Einstein and Friedmann universes without a cosmic string, whereas the second one is simply the Casimir energy of the electromagnetic field in these backgrounds, multiplied by a parameter λ=(1/α)−1, where α is a constant that codifies the presence of the cosmic string, and is related to its linear mass density, μ, by the expression α=1−Gμ. The Casimir free energy and the internal energy at a temperature different from zero, as well as the Casimir entropy, are given by similar sums. In the cases of the electromagnetic and massless spinor fields, the Casimir energy, free energy, internal energy, and Casimir entropy are also given by the sum of two terms, similarly to the previous cases, but now with both terms related to the same field. Using the results obtained concerning the mentioned thermodynamic quantities, their behavior at high and low temperatures limits are studied. All these results are particularized to the scenario in which the cosmic string is absent. Some discussions concerning the validity of the Nernst heat theorem are included as well.

General cubic interacting vertex for massless integer higher spin fields

We consider a massless higher spin field theory within the BRST approach and construct a general off-shell cubic vertex corresponding to irreducible higher spin fields of helicities s1,s2,s3. Unlike the previous works on cubic vertices, which do not take into account of the trace constraints, we use the complete BRST operator, including the trace constraints that describe an irreducible representation with definite integer helicity. As a result, we generalize the cubic vertex found in [14] and calculate the new contributions to the vertex, which contain additional terms with a smaller number space-time derivatives of the fields as well as the terms without derivatives.

Gravitational-wave polarizations in generic linear massive gravity and generic higher-curvature gravity

We study the polarizations of gravitational waves (GWs) in two classes of extended gravity theories. First, we formulate the polarizations in linear massive gravity (MG) with generic mass terms of non-Fierz-Pauli type by identifying all the independent variables that obey Klein-Gordon-type equations. The dynamical degrees of freedom (dofs) in the generic MG consist of spin-2 and spin-0 modes, the former breaking down into two tensor (helicity-2), two vector (helicity-1) and one scalar (helicity-0) components, while the latter just corresponding to a scalar. We find convenient ways of decomposing the two scalar modes of each spin into distinct linear combinations of the transverse and longitudinal polarizations with coefficients directly expressed by the mass parameters, thereby serving as a useful tool in measuring the masses of GWs. Then we analyze the linear perturbations of generic higher-curvature gravity (HCG) whose Lagrangian is an arbitrary polynomial of the Riemann tensor. On a flat background, the linear dynamical dofs in this theory are identified as massless spin-2, massive spin-2, and massive spin-0 modes. As its massive part encompasses the identical structure to the generic MG, GWs in the generic HCG provide six massive polarizations on top of the ordinary two massless modes. In parallel to MG, we find convenient representations for the scalar-polarization modes directly connected to the parameters of HCG. In this analysis, we employ two distinct methods; One takes full advantage of the partial equivalence between the generic HCG and MG at the linear level, whereas the other relies upon a gauge-invariant formalism. We confirm that the two results agree. We also discuss methods to determine the theory parameters by GW-polarization measurements. Our method does not require measuring the propagation speeds or the details of the waveforms of the GWs. [Abridged]

Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories

In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein–Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in f(R) theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background.

A calculation of the Weyl anomaly for 6D conformal higher spins

In this work we continue the study of the one-loop partition function for higher derivative conformal higher spin (CHS) fields in six dimensions and its holographic counterpart given by massless higher spin Fronsdal fields in seven dimensions.In going beyond the conformal class of the boundary round 6-sphere, we start by considering a Ricci-flat, but not conformally flat, boundary and the corresponding Poincaré-Einstein space-filling metric. Here we are able to match the UV logarithmic divergence of the boundary with the IR logarithmic divergence of the bulk, very much like in the known 4D/5D setting, under the assumptions of factorization of the higher derivative CHS kinetic operator and WKB-exactness of the heat kernel of the dual bulk field. A key technical ingredient in this construction is the determination of the fourth heat kernel coefficient b6 for Lichnerowicz Laplacians on both 6D and 7D Einstein manifolds. These results allow to obtain, in addition to the already known type-A Weyl anomaly, two of the three independent type-B anomaly coefficients in terms of the third, say c3 for instance.In order to gain access to c3, and thus determine the four central charges independently, we further consider a generic non Ricci-flat Einstein boundary. However, in this case we find a mismatch between boundary and bulk computations for spins higher than two. We close by discussing the nature of this discrepancy and perspectives for a possible amendment.

Conjugate spinor field equation for massless spin-$\frac{3}{2}$ field in de Sitter ambient space

The quantum field theory in de Sitter ambient space provide us with a comprehensivedescription of massless gravitational field.Using the gauge-covariant derivative in the de Sitter ambient space, the gauge invariant Lagrangian density has been found.In this paper, the equation of the conjugate spinor for massless spin-$\frac{3}{2}$ field is obtained by Euler-Lagrange equation. Then the field equation is written in terms of the Casimir operator of the de Sitter group. Finally, the gauge invariant field equation is presented.

Static response and Love numbers of Schwarzschild black holes

We derive the quadratic action for the physical degrees of freedom of massless spin-0, spin-1, and spin-2 perturbations on a Schwarzschild-(A)dS background in arbitrary dimensions. We then use these results to compute the static response of asymptotically flat Schwarzschild black holes to external fields. Our analysis reproduces known facts about black hole Love numbers — in particular that they vanish for all types of perturbation in four spacetime dimensions — but also leads to new results. For instance, we find that neutral Schwarzschild black holes polarize in the presence of an electromagnetic background in any number of spacetime dimensions except four. Moreover, we calculate for the first time black hole Love numbers for vector-type gravitational perturbations in higher dimensions and find that they generically do not vanish. Along the way, we shed some light on an apparent discrepancy between previous results in the literature, and clarify some aspects of the matching between perturbative calculations of static response on a Schwarzschild background and the point-particle effective theory.

Black hole perturbations of massive and partially massless spin-2 fields in (anti) de Sitter spacetime

We provide a systematic and comprehensive derivation of the linearized dynamics of massive and partially massless spin-2 particles in a Schwarzschild (anti) de Sitter black hole background, in four and higher spacetime dimensions. In particular, we show how to obtain the quadratic actions for the propagating modes and recast the resulting equations of motion in a Schrödinger-like form. In the case of partially massless fields in Schwarzschild de Sitter spacetime, we study the isospectrality between modes of different parity. In particular, we prove isospectrality analytically for modes with multipole number L = 1 in four spacetime dimensions, providing the explicit form of the underlying symmetry. We show that isospectrality between partially massless modes of different parity is broken in higher-dimensional Schwarzschild de Sitter spacetimes.

The eigenmodes for spinor quantum field theory in global de Sitter space–time

The mode solutions of the Dirac equation on N-dimensional de Sitter space–time (dSN) with (N − 1)-sphere spatial sections are obtained by analytically continuing the spinor eigenfunctions of the Dirac operator on the N-sphere (SN). The analogs of flat space–time positive frequency modes are identified, and a vacuum is defined. The transformation properties of the mode solutions under the de Sitter group double cover [Spin(N,1)] are studied. We reproduce the expression for the massless spinor Wightman two-point function in closed form using the mode-sum method. By using this closed-form expression and taking advantage of the maximal symmetry of dSN, we find an analytic expression for the spinor parallel propagator. The latter is used to construct the massive Wightman two-point function in closed form.

Cubic interaction vertices for massless higher spin supermultiplets in d = 4

We construct a range of supersymmetric cubic vertices for three massless higher spin supermultiplets in the four-dimensional space. We use frame-like multispinor formalism, which allows to avoid most of the technical difficulties and provides a uniform description for bosons and fermions. Our work is based on the so-called Fradkin-Vasiliev formalism for construction of the cubic vertices, which requires the non-zero cosmological constant. Thus we first construct the vertices in AdS space and then consider the flat limit. We show that the AdS supersymmetric vertex is a sum of four elementary vertices for supermultiplet components, while one of the vertices vanishes in the flat limit in agreement with the Metsaev’s classification.

Theory of 3F4D Universe (Beyond Standard Model of Particle Physics)

In this theory, “mass is equivalent to length of imaginary straight line segment” and “direction to imaginary line segment is intrinsic property of that particle which is Equivalent to its intrinsic spin”. With this concept, all fundamental particles, fermions and bosons are described as quanta imaginary string particles with a definite direction. For e.g. unidirectional imaginary straight line with fixed length are massive spin 1/2 fermions; while unidirectional imaginary quanta curved lines are massless spin 1 bosons. Thus, it gives co-relation between massless (curved imaginary line) and spin = 1 properties of boson as proved in QED theory. All fundamental particles of standard model and beyond standard model are arranged in one simple diagram in 3 folds (bottom fold, middle upper and lower folds and top fold) and are projected in 4th Imaginary Dimension in order of decreased in Mass from TeV to approx. 0 eV. This theory is beyond standard model because it predicts new fundamental particles viz. dark matter (spin = 0 massive boson) along with gravitons (spin = 2, massless bosons); 4th pair of neutrinos, vertical massless boson (VMB) particles and tri-axis massive boson (spin = 0) particle. The discovery of these new particles will act as solid proof to this theory. With this 3F4D representation of the universe at an atomic and sub-atomic level, it solves lots of current problems of SM of particle physics like matter-antimatter asymmetry, origin of mass of hadrons like protons, origin of mass and L.H. nature for neutrinos, wave-particle duality of particles, etc. giving true insight of fundamental particles. With proving that, dark matter is not a quanta particle, rather it is a single entity and spreads/expands throughout the universe in the form of “web of spider”, it shows space-time is not empty, but it is filled with Continuous lines of Dark Matter and we, materialistic massive objects are floating/sailing w.r.t. current of this vast ocean. Correlation of its continuity with time gives new a definition to time: “Time is neither Illusion nor 4th Dimension, but, it represents Continuous Flow of Single Entity, Dark Matter”. Space-time is not Empty and is filled with massive dark matter, hence, we have to add more terms to newtonian gravitational equation to account for gravitational strength of mass of surrounding dark matter which represents curvature of space-time in terms of Increase in its mass-density w.r.t. to mass-density of flat universe. Finally, using an empirical formula (h = k*c*Q; k = boltzmann’s constant = mass in TeV range) and inverse relation of mass-density of DM with age of the universe (H2 = Constant&#8226G&#8226Mass-Density of DM); Unification of Gravity at TeV is achieved without consideration of “Gravitational Constant, G”, hence, Planck’s Scale is not required.

Interplay between neutrino and gravity portals for FIMP dark matter

In the classic type I seesaw mechanism with very heavy right-handed (RH) neutrinos, it is possible to account for dark matter via RH neutrino portal couplings to a feebly interacting massive particle (FIMP) dark sector. However, for large RH neutrino masses, gravity can play an important role. We study the interplay between the neutrino portal through the right-handed neutrinos and the gravity portal through the massless spin-2 graviton in producing dark matter particles in the early universe. As a concrete example, we consider the minimal and realistic Littlest Seesaw model with two RH neutrinos, augmented with a dark scalar and a dark fermion charged under a global U(1)D dark symmetry. In the model, the usual seesaw neutrino Yukawa couplings and the right-handed neutrino masses (the lightest being about 5× 1010 GeV) are fixed by neutrino oscillations data and leptogenesis. Hence, we explore the parameter space of the two RH neutrino portal couplings, the two dark particle masses and the reheating temperature of the universe, where the correct dark matter relic abundance is achieved through the freeze-in mechanism. In particular, we highlight which class of processes dominate the dark matter production. We find that, despite the presence of the gravity portal, the dark matter production relies on the usual seesaw neutrino Yukawa coupling in some regions of the parameter space, so realising a direct link between dark matter and neutrino phenomenology. Finally, we report the threshold values for the neutrino portal couplings below which the neutrino portal is irrelevant and the Planckian Interacting Dark Matter paradigm is preserved.

Second-order charge currents and stress tensor in a chiral system

We study Wigner equations for massless spin-$1/2$ charged fermions at global equilibrium in static and uniform vorticity and electromagnetic fields. The Wigner functions can be solved order by order from Wigner equations through the power expansion of the vorticity and electromagnetic fields. The nondissipative charge currents and the stress tensor up to the second order can be obtained from Wigner functions. The charge and energy densities and the pressure have contributions from vorticity and electromagnetic fields at the second order. The vector and axial Hall currents can be induced along the direction orthogonal to vorticity and electromagnetic fields at the second order. We also find that the trace anomaly emerges naturally in renormalization of the stress tensor by including quantum corrections from electromagnetic fields.

Positivity bounds and the massless spin-2 pole

The presence of a massless spin-2 field in an effective field theory results in a $t$-channel pole in the scattering amplitudes that precludes the application of standard positivity bounds. Despite this, recent arguments based on compactification to three dimensions have suggested that positivity bounds may be applied to the $t$-channel pole subtracted amplitude. If correct this would have deep implications for UV physics and the Weak Gravity Conjecture. Within the context of a simple renormalizable field theory coupled to gravity we find that applying these arguments would constrain the low-energy coupling constants in a way which is incompatible with their actual values. This contradiction persists on deforming the theory. Further enforcing the $t$-channel pole subtracted positivity bounds on such generic renormalizable effective theories coupled to gravity would imply new physics at a scale parametrically smaller than expected, with far reaching implications. This suggests that generically the standard positivity bounds are inapplicable with gravity and we highlight a number of issues that impinge on the formulation of a three-dimensional amplitude which simultaneously satisfies the required properties of analyticity, positivity and crossing symmetry. We conjecture instead a modified bound that ought to be satisfied independently of the precise details of the high energy completion.

A vector field method for some nonlinear Dirac models in Minkowski spacetime

Firstly we use the Lie derivatives of spinors with respect to Killing vector fields and conformal Killing vector fields to obtain the generalized commuting vector field set adapted to the Dirac operator. By the conservation law of the charge current and total angular momentum, as well as the weighted Sobolev estimates, it gives the optimal decay for the linear massless spinor fields and more decay for certain decomposition parts in any dimensions. Moreover, by exploiting the Dirac null structure, we also show the small data global existence and asymptotic decay properties for some well-known nonlinear models with cubic nonlinearities in space dimension two and quadratic nonlinearities in space dimension three.