Universal Yang-Mills action on four-dimensional manifolds

The usual action of the Yang-Mills theory is given by the quadratic form of curvatures of a principal G bundle defined on four-dimensional manifolds. The nonlinear generalization which is known as the Born-Infeld action has been given. In this paper we give another nonlinear generalization on four-dimensional manifolds and call it a universal Yang-Mills action. The advantage of our model is that the action splits automatically into two parts consisting of self-dual and anti-self-dual directions, that is, we have automatically the self-dual and anti-self-dual equations without solving the equations of motion as in usual case. Our method may be applicable to recent non-commutative Yang-Mills theories studied widely.