Non-Abelian Born–Infeld action, geometry and supersymmetry

Abstract

In this work, we propose a new non-abelian generalization of the BornInfeld lagrangian. It is based on a geometrical property of the abelian Born-Infeld lagrangian in its determinantal form. Our goal is to extend the abelian second type Born-Infeld action to the non-abelian form preserving this geometrical property, that permits to compute the generalized volume element as a linear combination of the components of metric and the Yang-Mills energy-momentum tensors. Under BPS-like condition, the action proposed reduces to that of Yang-Mills theory, independently of the gauge group. New instanton-wormhole solution and static and spherically symmetric solution in curved space-time for a SU(2) isotopic ansatz is solved and the N=1 supersymmetric extension of the model is performed.

Unified Field Theoretical Models from Generalized Affine Geometries II

“…Precisely this relation is directly connected with the relation of the spin and torsion fields. The solution of this model is explicitly compared with our previous ones of references [3,4] and we find that: (i) the torsion is not identified directly with the Yang Mills type strength field, (ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact lead the identification between derivatives of the scale factor a with the components of the torsion in order to allows the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), (iii) this compatibility condition precisely mark the fact that local gauge covariance, coordinate independence and arbitrary space time geometries are harmonious concepts and (iv) of two possible structures of the torsion the "tratorial" form (the only one studied here) forbids wormhole configurations, leading only, cosmological instanton space-time in eternal expansion.…”

“…Section 3 is devoted to the analysis and reduction of the dynamical equations of the model. The exact solution, in the context of references [3,4], is obtained and analyzed from the geometrical and topological point of view in Sect. 4.…”

Fermion Interactions, Cosmological Constant and Space-Time Dimensionality in a Unified Approach Based on Affine Geometry

“…In that paper, the effective 4-fermion interaction was focused on the case of neutrinos endowed with non-standard interactions. These are a natural outcome of many neutrino mass models [23] and can be of two types: flavour-changing (FC) and non-universal (NU). As it is well known, see-saw-type models leads to a non-trivial structure of the lepton mixing matrix characterizing the charged and neutral current weak interactions.…”

“…As pointed out in references [19][20][21][22][23][24], the torsion vector h = h α dx α (the 4-dimensional dual of the torsion field T βγδ ) plays multiple roles and can be constrained in several different physical situations. Mathematically, it is defined by the Hodge-de Rham decomposition given by the 4-dimensional Helmholtz theorem which states:…”

“…It is possible to show [19][20][21][22][23][24] that to derive the Dirac equation, one needs, as starting point, the symmetric part of the gravitational field equations derived from δ g L g = 0, that is…”