New spinor fields on Lorentzian 7-manifolds

Abstract

This paper deals with the classification of spinor fields according to the bilinear covariants in 7 dimensions. The previously investigated Riemannian case is characterized by either one spinor field class, in the real case of Majorana spinors, or three non-trivial classes in the most general complex case. In this paper we show that by imposing appropriate conditions on spinor fields in 7d manifolds with Lorentzian metric, the formerly obtained obstructions for new classes of spinor fields can be circumvented. New spinor fields classes are then explicitly constructed. In particular, on 7-manifolds with asymptotically flat black hole background, these spinors can define a generalized current density which further defines a time Killing vector at the spatial infinity. arXiv:1508.01357v2 [hep-th]

The Theory of Local Mass Dimension One Fermions of Spin One Half

“…The Brazilian-Italian group of Roldão da Rocha, Hoff da Silva, Bueno Rogerio, Cavalcanti, Bonora, Fabbri, Silva-Neto, Bernardini, J. G. Pereira, and Coronado Villalobos, besides examining such important topics as Hawking radiation of mass dimension one fermions [73], continue to develop mathematical physics underlying Elko [73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89]. Of these we draw particular attention to mass-dimension transmuting operators considered in [75,77].…”

The Graf Product: A Clifford Structure Framework on the Exterior Bundle

“…[10,11], where new classes of spinor fields have been derived in several dimensions and signatures in Refs. [12,13,14,15]. We are going to employ the setup here developed to studied further classes of spinor fields in manifolds of signature (9,0), being beyond of the scope of this work.…”

New spinor classes on the Graf-Clifford algebra

“…5 Spinor classes on signature (1,2) New classes of spinors have been found under the formalism of the Graf product and the Fierz identities, for signatures (7, 0), (6, 1), and (1,4), respectively in Refs. [14][15][16]. In this section we will find three non-trivial new classes of spinor fields on 3-dimensional pseudo-Riemannian manifolds with signature (1, 2), employing this method.…”

“…The geometric Fierz identities are constraints on the bilinear covariants, yielding to classify spinors fields on any simply connected manifold with spin structure [5]. Recently, a classification of spinor fields on Lorentzian [14] and Riemannian [15] 7-manifolds has been constructed, emulating the Lounesto's classification. It introduces new classes of spinors and new fermionic solutions in supergravity, regarding, in particular, its AdS 5 × S 5 [16,22] and AdS 4 × S 7 [14] compactifications.…”

“…Having constructed new classes of spinors, implicitly using the Graf product and the geometric Fierz identities [5], for signatures (7,0), (6,1), and (1,4) [14][15][16], our main aim here is to derive new classes of spinors on a Lorentzian space with signature (1,2), employing this method, and also to construct pinors in signature (9,0). This last case is naturally linked to spinors in R 1,9 , as elements that carry the irreducible representation of the group Spin 1,9 , whose Lie algebra so (1,9) spin (1,9) is isomorphic to the Lorentz-like Lie algebra sl (2, O).…”