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, which permits us to compute the generalized volume element as a linear combination of the components of metric and the Yang-Mills energy-momentum tensors. Under the BPS-like condition, the action proposed reduces to that of the Yang-Mills theory, independently of the gauge group. New instanton-wormhole solution and static and spherically symmetric solution in curved spacetime for an SU(2) isotopic ansatz are solved and the N = 1, supersymmetric extension of the model is performed.