Non-Abelian Born-Infeld action, geometry and supersymmetry

In this work, we propose a new non-abelian generalization of the Born- Infeld 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.