From dipole spinors to a new class of mass dimension one fermions

In this paper, we investigate a quite recent new class of spin one-half fermions, namely Ahluwalia class-7 spinors, endowed with mass dimensionality 1 rather than 3/2, being candidates to describe dark matter. Such spinors, under the Dirac adjoint structure, belongs to the Lounesto’s class-6, namely, dipole spinors. Up to our knowledge, dipole spinor fields have Weyl spinor fields as their most known representative, nonetheless, here we explore the dark counterpart of the dipole spinors, which represents eigenspinors of the chirality operator.

Weyl doubling

We study a host of spacetimes where the Weyl curvature may be expressed algebraically in terms of an Abelian field strength. These include Type D spacetimes in four and higher dimensions which obey a simple quadratic relation between the field strength and the Weyl tensor, following the Weyl spinor double copy relation. However, we diverge from the usual double copy paradigm by taking the gauge fields to be in the curved spacetime as opposed to an auxiliary flat space.We show how for Gibbons-Hawking spacetimes with more than two centres a generalisation of the Weyl doubling formula is needed by including a derivative-dependent expression which is linear in the Abelian field strength. We also find a type of twisted doubling formula in a case of a manifold with Spin(7) holonomy in eight dimensions.For Einstein Maxwell theories where there is an independent gauge field defined on spacetime, we investigate how the gauge fields determine the Weyl spacetime curvature via a doubling formula. We first show that this occurs for the Reissner-Nordström metric in any dimension, and that this generalises to the electrically-charged Born-Infeld solutions. Finally, we consider brane systems in supergravity, showing that a similar doubling formula applies. This Weyl formula is based on the field strength of the p-form potential that minimally couples to the brane and the brane world volume Killing vectors.

Peeling property and asymptotic symmetries with a cosmological constant

This paper establishes two things in an asymptotically (anti-)de Sitter spacetime, by direct computations in the physical spacetime (i.e. with no involvement of spacetime compactification): (1) The peeling property of the Weyl spinor is guaranteed. In the case where there are Maxwell fields present, the peeling properties of both Weyl and Maxwell spinors similarly hold, if the leading order term of the spin coefficient [Formula: see text] when expanded as inverse powers of [Formula: see text] (where [Formula: see text] is the usual spherical radial coordinate, and [Formula: see text] is null infinity, [Formula: see text]) has coefficient [Formula: see text]. (2) In the absence of gravitational radiation (a conformally flat [Formula: see text]), the group of asymptotic symmetries is trivial, with no room for supertranslations.

Fermion Colour and Flavour Originating from Multiple Representations of the Lorentz Group and Clifford Algebra

Where do such fermion properties as colour and flavour come from? We attempt to give a possible answer to this question in our paper. For that purpose we use the reducible (1/2,1/2) representation of the Lorentz group. Then the fermion corresponds to a doublet, each component of which can be described by the standard Dirac equation. In this way we conclude that quark and lepton, when being considered as doublets, originate from the discussed multiple representations of the Lorentz group (LG) and the related Clifford algebra. In particular the threefold colour degree of freedom emerges naturally, and similarly the threefold generation degree, both being enabled essentially by the fact that the SU(2) group has three generators given by the Pauli matrices. The Dirac spinor, or for zero mass the chiral Weyl spinor, remains the building block of that theory.

A note on supersymmetries in AdS5/CFT4

The [Formula: see text] superconformal algebra is derived from the symmetry transformations of fields in the [Formula: see text] SYM action in [Formula: see text]. We use a Majorana–Weyl spinor in [Formula: see text] instead of four Weyl spinors in [Formula: see text]. This makes it transparent to relate generators of the [Formula: see text] superconformal algebra to those of the super-[Formula: see text] algebra. Especially, we obtain the concrete map from the supersymmetries [Formula: see text] and conformal supersymmetries [Formula: see text] in [Formula: see text] SYM to the supersymmetries [Formula: see text] in the [Formula: see text] background.

Modifying the theory of gravity by changing independent variables

We study some particular modifications of gravity in search for a natural way to unify the gravitational and electromagnetic interaction. The certain components of connection in the appearing variants of the theory can be identified with electromagnetic potential. The methods of adding matter in the form of scalar and spinor fields are studied. In particular, the expansion of the local symmetry group up to GL(2,C) is explored, in which equations of Einstein, Maxwell and Dirac are reproduced for the theory with Weyl spinor.

Feynman rules for Weyl spinors with mixed Dirac and Majorana mass terms

We present a basic formalism for using the Weyl spinor notation in Feynman rules. We focus on Weyl spinors with mixed Dirac and Majorana mass terms. To clarify the definitions we derive the Feynman rules from the path integral and present two examples: loop corrections for a fermion propagator and a tree level analysis of a seesaw toy model.

3+1DMassless Weyl Spinors from Bosonic Scalar-Tensor Duality

We consider the fermionization of a bosonic-free theory characterized by the3+1Dscalar-tensor duality. This duality can be interpreted as the dimensional reduction, via a planar boundary, of the4+1Dtopological BF theory. In this model, adopting the Sommerfield tomographic representation of quantized bosonic fields, we explicitly build a fermionic operator and its associated Klein factor such that it satisfies the correct anticommutation relations. Interestingly, we demonstrate that this operator satisfies the massless Dirac equation and that it can be identified with a3+1DWeyl spinor. Finally, as an explicit example, we write the integrated charge density in terms of the tomographic transformed bosonic degrees of freedom.

TOPOLOGICAL FOUR-DIMENSIONAL GRAVITY AND KODAMA STATE BEYOND INSTANTONS

By using the two-component spinor formalism and the symplectic geometry of the phase space, it is shown that the Kodama state actually exist within a topological phase where the Weyl spinor does not vanish. This topological phase, belonging to the complete topological sector of general relativity (GR), is bigger than the one associated with gravitational instantons. The conditions of projection onto the sector of gravitational instantons are discussed as well.

Four–dimensional metrics conformal to Kähler

We derive some necessary conditions on a Riemannian metric (M, g) in four dimensions for it to be locally conformal to Kähler. If the conformal curvature is non anti–self–dual, the self–dual Weyl spinor must be of algebraic type D and satisfy a simple first order conformally invariant condition which is necessary and sufficient for the existence of a Kähler metric in the conformal class. In the anti–self–dual case we establish a one to one correspondence between Kähler metrics in the conformal class and non–zero parallel sections of a certain connection on a natural rank ten vector bundle over M. We use this characterisation to provide examples of ASD metrics which are not conformal to Kähler.We establish a link between the ‘conformal to Kähler condition’ in dimension four and the metrisability of projective structures in dimension two. A projective structure on a surface U is metrisable if and only if the induced (2, 2) conformal structure on M = TU admits a Kähler metric or a para–Kähler metric.