Rarita Schwinger Research Articles

De-Higgsing in eleven-dimensional supergravity on the squashed S 7

Abstract In this paper we construct the subset of modes on S 7 that are relevant in the compactification of eleven-dimensional supergravity on a squashed S 7 when restricted to the sector that comprises singlets under the S p ( 1 ) × S p ( 2 ) isometry of the squashed sphere. Some of the properties of these modes, connected to the transition from the round S 7 to the squashed S 7, are analysed in detail. Special features of the Rarita–Schwinger operator, described in earlier work by Buchdahl, are explained and related to properties of the squashed S 7 operator spectrum obtained in previous work by the authors. We then discuss how the singlet modes give rise to supermultiplets in the left-squashed case, the phenomenon of de-Higgsing, and what happens to the AdS4 fields in these supermultiplets under an orientation reversal (‘skew-whiffing’) of the squashed S 7. Finally, we consider the possible choices of boundary conditions that appear for some of these fields in AdS4 in the case of the right-squashed non-supersymmetric compactification, and how these choices may affect the stability of the gravity theory.

Fermionic greybody factors and quasinormal modes of black holes in Kalb–Ramond gravity

In non-minimally coupled Kalb–Ramond (KR) fields, the vacuum expectation value (VEV) leads to spontaneous local Lorentz symmetry violation, resulting in static spherically symmetric solution. In this solution, fermionic greybody factors (GFs) and quasinormal modes (QNMs) are investigated. First, we study the wave dynamics of fermions using the Dirac and Rarita–Schwinger equations. We have derived the equations of effective potential for fermions with different spins. The fermionic GFs radiated by the black holes (BHs) are calculated using rigorous bounds as well as semi-analytic methods. The fermionic QNM of spin- 1/2 of the BHs in the KR gravity was analyzed using the sixth order WKB method. Furthermore, we discuss how Lorentz violating (LV) parameters impact GFs and QNMs. According to our results, the effective potential curve increases significantly when the LV parameter value γ is high. Thus, as the LV parameter γ increases, the bound of the GF and the QNM’s wave oscillation frequency will increase, while the decay rate will slow down.

Pin(2)-Equivariance Property of the Rarita–Schwinger–Seiberg–Witten Equations

Pin(2)-Equivariance Property of the Rarita–Schwinger–Seiberg–Witten Equations

Sources of torsion in Poincarè gauge gravity

We study sources for torsion in Poincarè gauge theory in any dimension, signature, and spin. We find that symmetric kinetic terms for non-Yang–Mills bosonic fields of arbitrary rank drive torsion. Our detailed discussion of spin-3/2 Rarita–Schwinger fields shows that they source all independent parts of the torsion. We develop systematic notation for spin-(2k+1)/2 fields and find the spin tensor for arbitrary k in n ge 2k+1 dimensions. For k>0 there is a novel direct coupling between torsion and spinor fields. We also cast the well-known gauge relation between the canonical and Belinfante–Rosenfield energy tensors in terms of different choices of independent variables.

Anomaly inflow of Rarita–Schwinger field in 3 dimensions

Anomaly inflow of Rarita–Schwinger field in 3 dimensions

Hawking radiation of rotating BTZ black hole based on modified dispersion relation and Rarita–Schwinger equation

In this paper, tunneling of fermions from rotating BTZ black hole is investigated using modified dispersion relation (MDR) and Rarita–Schwinger equation. The effect of MDR on the tunneling of fermions raises the Hawking temperature of rotating BTZ black hole. It is observed that the modified Hawking temperature of the black hole depends not only on the radial parameters of the black hole but also on the angular parameters of the black hole and the coupling constant [Formula: see text]. Further, the entropy and the heat capacity of the black hole are also studied.

Greybody factors emitted by a regular black hole in a non-minimally coupled Einstein–Yang–Mills theory

In this paper, we study the greybody factors (GFs) for fermions with different spins and bosons in the regular black hole (BH) predicted by a non-minimal Einstein–Yang–Mills (EYM) theory. We investigate the effect of magnetic charge on effective potentials and GFs. For this purpose, we consider the Dirac and Rarita–Schwinger, as well as Klein–Gordon equations. First, we study the Dirac equation in curved spacetime for massive and massless spin-1/2 fermions. We then separate the Dirac equation into sets of radial and angular equations. Using the analytical solution of the angular equation, the Schrödinger-like wave equations with potentials are derived by decoupling the radial wave equations via the tortoise coordinate. We also consider the Rarita–Schwinger equation for massless spin-3/2 fermions and derive the one-dimensional Schrödinger wave equation with gauge-invariant effective potential. For bosons, we study the Klein–Gordon equation in the regular non-minimal EYM BH. Afterward, semi-analytic methods were used to calculate the fermionic and bosonic GFs. Finally, we discuss the graphical behavior of the obtained effective potentials and bounds on the GFs. According to graphs, the GF is highly influenced by the potential’s shape, which is determined by the parameterization of the model. This is in line with quantum theory.

Fermionic Greybody Factors in Schwarzschild Acoustic Black Holes

In Schwarzschild acoustic black hole (SABH) spacetime, we investigate the wave dynamics for the fermions. To this end, we first take into account the Dirac equation in the SABH by employing a null tetrad in the Newman–Penrose (NP) formalism. Then, we consider the Dirac and Rarita–Schwinger equations, respectively. The field equations are reduced to sets of radial and angular equations. By using the analytical solution of the angular equation set, we decouple the radial wave equations and obtain the one-dimensional Schrödinger-like wave equations with their effective potentials. The obtained effective potentials are graphically depicted and analyzed. Finally, we investigate the fermionic greybody factors (GFs) radiated by the SABH spacetime. A thorough investigation is conducted into how the acoustic tuning parameter affects the GFs of the SABH spacetime. Both the semi-analytic WKB method and bounds for the GFs are used to produce the results, which are shown graphically and discussed.

Monstrous M-Theory

In 26+1 space–time dimensions, we introduce a gravity theory whose massless spectrum can be acted upon by the Monster group when reduced to 25+1 dimensions. This theory generalizes M-theory in many respects, and we name it Monstrous M-theory, or M2-theory. Upon Kaluza–Klein reduction to 25+1 dimensions, the M2-theory spectrum irreducibly splits as 1 ⊕ 196,883, where 1 is identified with the dilaton, and 196,883 is the dimension of the smallest non-trivial representation of the Monster. This provides a field theory explanation of the lowest instance of the Monstrous Moonshine, and it clarifies the definition of the Monster as the automorphism group of the Griess algebra by showing that such an algebra is not merely a sum of unrelated spaces, but descends from massless states for M2-theory, which includes Horowitz and Susskind’s bosonic M-theory as a subsector. Further evidence is provided by the decomposition of the coefficients of the partition function of Witten’s extremal Monster SCFT in terms of representations of SO24, the massless little group in 25+1; the purely bosonic nature of the involved SO24-representations may be traced back to the unique feature of 24 dimensions, which allow for a non-trivial generalization of the triality holding in 8 dimensions. Last but not least, a certain subsector of M2-theory, when coupled to a Rarita–Schwinger massless field in 26+1, exhibits the same number of bosonic and fermionic degrees of freedom; we cannot help but conjecture the existence of a would-be N=1 supergravity theory in 26+1 space–time dimensions.

Scattering of complex gravitino test fields from a gravitational pulse

Gravitational pulse waves are defined as step functions at the boundaries. In this setting, linearized Rarita–Schwinger equations are precisely solved in Rosen coordinates. It is found that the gravitino’s energy–momentum varies with the sandwich wave’s shape. The gravitino’s energy density will decrease as it crosses the sandwich wave at the test field level since the background won’t change.

Generalized Mathisson–Papapetrou–Tulczyjew–Dixon equations

We derive two generalizations of Mathisson–Papapetrou–Tulczyjew–Dixon equations from Casalbuoni–Brink–Schwarz type pseudoclassical Lagrangians of Majorana spinors on a Riemann–Cartan spacetime. One has an additional gauge freedom, which makes the equations of motion also be a generalization of Wong’s equations. The other is a spinor model coupled with a Rarita–Schwinger field to preserve the supersymmetry. The coupling to the torsion is modified due to the existence of the Rarita–Schwinger field. In both extensions, the Tulczyjew condition is automatically satisfied.

On commutator-based linearization of vector-spinor nonlinear supersymmetry and Rarita–Schwinger fields

In this paper, we discuss the linearization of vector-spinor (spin-3/2) nonlinear supersymmetry (vsNLSUSY) transformations for both [Formula: see text] and [Formula: see text]-extended SUSY in flat spacetime based on the commutator algebra by using functionals (composites) of spin-3/2 Nambu–Goldstone (NG) fermions, which are expressed as simple products of powers of the spin-3/2 NG fermions and a fundamental determinant in the vsNLSUSY theory. We define basic component fields by means of those functionals in a linearized vsSUSY theory including spin-3/2 fields, general auxiliary ones and a [Formula: see text]-term. The general forms of linear (rigid) vsSUSY transformations for the component fields are determined uniquely from the commutator-based linearization procedure. By considering appropriate recombinations of the functionals of the spin-3/2 NG fermions for [Formula: see text] SUSY, we find that variations of the recombinations under the vsNLSUSY transformations include linear spin-1/2 SUSY ones of spin-[Formula: see text] fields with [Formula: see text] gauge invariance. The spinorial gauge invariance of the Rarita–Schwinger action in the linearization process is also discussed together with the [Formula: see text] gauge invariance.

Asymptotic symmetries at null-infinity for the Rarita–Schwinger field with magnetic term

In this paper we study the magnetic charges of the free massless Rarita–Schwinger field in four dimensional asymptotically flat space-time. This is the first step towards extending the study of the dual BMS charges to supergravity. The magnetic charges appear due to the addition of a boundary term in the action. This term is similar to the theta term in Yang–Mills theory. At null-infinity an infinite dimensional algebra is discovered, both for the electric and magnetic charge.

Manifolds with Many Rarita\u2013Schwinger Fields

The Rarita–Schwinger operator is the twisted Dirac operator restricted to nicefrac 32-spinors. Rarita–Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita–Schwinger fields tends to infinity. These manifolds are either simply connected Kähler–Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi–Yau manifolds of even complex dimension with more linearly independent Rarita–Schwinger fields than flat tori of the same dimension.

Consistency of M-Theory on Non-Orientable Manifolds

Abstract We prove that there is no parity anomaly in M-theory in the low-energy field theory approximation. Our approach is computational. We determine the generators for the 12-dimensional bordism group of pin manifolds with a w1-twisted integer lift of w4; these are the manifolds on which Wick-rotated M-theory exists. The anomaly cancellation comes down to computing a specific η-invariant and cubic form on these manifolds. Of interest beyond this specific problem are our expositions of computational techniques for η-invariants, the algebraic theory of cubic forms, Adams spectral sequence techniques and anomalies for spinor fields and Rarita–Schwinger fields.

Chiral Separation Effect in Rarita–Schwinger–Weyl Semimetals

The chiral separation effect is studied for spin-3/2 fermions. The main emphasis is put on Rarita–Schwinger–Weyl semimetals. The relation between the predicted effect and the axial anomaly is discussed.

Структура плоских волн для частицы со спином 3/2, безмассовый случай, калибровочная симметрия

The structure of plane wave solutions for a relativistic spin 3/2 particle described by a 16-component vector-bispinor is studied. In the massless case, two representations of the equation are used: in the Rarita–Schwinger basis and in a special second basis in which the wave equation contains the Levi–Civita tensor. In this second basis, the existenceof trivial solutions in the form of a gradient on arbitrary bispinor becomes obvious. It is shown that he general solution of the massless equation consists of 6 linearly independent solutions. It is explicitly proved that four of them can be identified with gauge solutions and, therefore, can be removed as non-physical. The exclusion procedure of gaugecomponents is carried out in both representations of the massless equation.

Coexistence of Rarita–Schwinger–Weyl fermion and spin-1 excitation in Bi4Ni6S4

In addition to Dirac and Weyl fermions, exotic massless fermions with non-zero Berry curvature fluxes may exist in condensed matter systems under the protection of crystal symmetry, for example, spin-1 excitations with threefold degeneracy and spin-3/2 Rarita–Schwinger–Weyl fermions with fourfold degeneracy. More recently, the theory of topological quantum chemistry has provided us with a convenient way to find the existence of these quasi-particles. Herein, we have found a space group (No. 199) that may have both spin-1 excitations and spin-3/2 Rarita–Schwinger–Weyl fermions near the Fermi level. By using the ab initio density functional theory, we show that these unconventional quasi-particles mentioned above coexist in Bi4Ni6S4 in space group [Formula: see text] (No. 199), when spin-orbit coupling is considered. Their non-trivial topology results in a series of Fermi arcs connecting the projection of these excitations on (001) surface.

Modification to tunneling radiation of arbitrary spin fermions in stationary axisymmetric Sen black hole space–time

Considering the modified Lorentz dispersion relation, combined with the Dirac equation and Rarita–Schwinger equation of fermions in stationary axisymmetric Sen black hole space–time, the fermion tunneling radiation of the black hole is modified accurately, and meaningful physical quantities such as the modified fermion tunneling rate, event horizon temperature, and entropy of the black hole are obtained. The discussion of the conclusions shows that the effect of the Lorentz dispersion relation and Lorentz violation theory on particle dynamics must be considered in curved space–time during the study of quantum theory and Hawking tunneling radiation.

Research on the semiclassical theory and Hawking tunneling radiation of nonstationary Kerr black hole

In this paper, the tunneling radiations of spin 1/2 and spin 3/2 fermions from the nonstationary Kerr black hole are investigated. First, according to the Dirac equation and the Rarita–Schwinger equation, the Hamilton–Jacobi equations for spin 1/2 and 3/2 fermions are derived. Then, the tunneling behavior of fermions on the event horizon of the black hole is investigated. Finally, the thermodynamic properties of the nonstationary Kerr black hole are obtained.