Related papers: Rozenfeld's Geometric Approach to Spinors
We investigate the properties of the Extended Fock Basis (EFB) of Clifford algebras introduced in [1]. We show that a Clifford algebra can be seen as a direct sum of multiple spinor subspaces that are characterized as being left…
We give a detailed account of the geometric correspondence between a smooth complex projective quadric hypersurface $\mathcal{Q}^n$ of dimension $n \geq 3$, and its twistor space $\mathbb{PT}$, defined to be the space of all linear…
We construct new infinite classes of Euclidean supersymmetric solutions of four dimensional minimal gauged supergravity comprising a $U (1) \times U (1)$-invariant asymptotically locally hyperbolic metric on the total space of orbifold line…
Based on the revealed hidden supergroup structure, we develop a new approach to the Hubbard model. We reveal a relation of even Hubbard operators to the spinor representation of the generators of the rotation group of four-dimensional…
Spinorial geometry methods are used to classify solutions admitting Majorana Killing spinors of the minimal 4-dimensional supergravity in neutral signature, with vanishing cosmological constant and a single Maxwell field strength. Two…
Jordan geometries are defined as spaces equipped with point reflections depending on triples of points, exchanging two of the points and fixing the third. In a similar way, symmetric spaces have been defined by Loos (Symmetric Spaces I,…
Conics in the Euclidean space have been known for their geometrical beauty and also for their power to model several phenomena in real life. It usually happens that when thinking about the conics in a semi-Riemannian manifold, the equations…
Spinor fields are considered in a generally covariant environment where they can be written in the polar form. The polar form is the one in which spinorial fields are expressed as a module times the exponential of a complex pseudo-phase,…
The supersymmetric solutions of N=2, D=4 minimal ungauged and gauged supergravity are classified according to the fraction of preserved supersymmetry using spinorial geometry techniques. Subject to a reasonable assumption in the…
Developing a theory for quantum gravity is one of the big open questions in theoretical high-energy physics. Recently, a tensor model approach has been considered that treats tensors as the generators of commutative non-associative…
By using symplectic Majorana spinors as Grassmann coordinates in a superspace associated with the supersymmetric extension of the isometry group on the spherical surface S_2, it proves possible to formulate supersymmetric models on S_2…
A Sasakian quasi-Killing spinor (SqK-spinor), which is a generalization of a Killing spinor on Sasakian manifolds, was defined in \cite{Kim Friedrich 2000}.The purpose of this paper is to study in detail SqK-spinors on three-dimensional…
Coupling spinor fields to the gravitational field, in the setting of general relativity, is standardly done via the introduction of a vierbein field and the (associated minimal) spin connection field. This makes three types of indices…
We consider superconformal and supersymmetric field theories on four-dimensional Lorentzian curved space-times, and their five-dimensional holographic duals. As in the Euclidean signature case, preserved supersymmetry for a superconformal…
Spinorial geometry techniques have recently been used to classify all half supersymmetric solutions in gauged five dimensional supergravity with vector multiplets. In this paper we consider solutions for which at least one of the Killing…
Motivated by the relationship between orthogonal complex structures and spure spinors, we define twisted partially pure spinors in order to characterize spinorially subspaces of Euclidean space endowed with a complex structure.
In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel…
We interpret an open orbit in a 32-dimensional representation space of Spin(9,1) x SL(2,R) as a substitute for the non-existent group of invertible 2x2 matrices over the octonions and study various natural homogeneous subspaces. The…
Euclidean special geometry has recently been investigated in the context of Euclidean supersymmetric theories with vector multiplets. In the rigid case, the scalar manifold is described by affine special para-Kahler geometry while the…
We propose methods towards a systematic determination of d dimensional curved spaces where Euclidean field theories with rigid supersymmetry can be defined. The analysis is carried out from a group theory as well as from a supergravity…