# Spinor fields on the bulk and on compactified dimensions

## TL;DR

This paper classifies fermionic spinor fields in supergravity contexts, exploring their properties on bulk and compactified spaces, and relates these classifications to physical phenomena like black hole invariants and brane generation.

## Contribution

It introduces a new classification scheme for spinor fields in supergravity, deriving Lagrangians and analyzing their implications on black holes and compactified dimensions.

## Key findings

- Identified Lagrangian terms for free spinor fields in seven-dimensional compactified spaces.
- Linked bilinear covariants of fermionic fields to invariants of axisymmetric black holes.
- Discovered that flag-dipole spinors do not generate branes but degenerate into dipole spinors.

## Abstract

This work has as the main aim to explore the nature of the fermionic fields, through a classification of spinor fields about physical space of interest, such as the bulk and the compactified space $S^7$ from the supergravity theories. This classification has an extreme utility in the exploration and in the search for new type of particles, whose observables correspond to bilinear covariants. In this way, these fields are classified into classes, through constraints obtained by means of the Fierz-Pauli-Kofink identities and the bilinear symmetries. We found the Lagrangian terms for the free spinor fields on spaces of seven compactified dimension in supergravity and, as application of our spinor fields classification on the bulk, we associate the invariants on axisymmetric black holes to the components of the bilinear covariants of the correspondent fermionic field. Besides, we found that a type of spinor denominated flag-dipole does not generate a brane, but degenerate itself in other type of spinor called dipole and, in compactification theories, we obtained the expression to the quantum field on compactified spaces for low energies in terms of creation and annihilation operators.