Narrow Results

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.

In this short report, a brief introduction to Arkani-Hamed, Cohen, Georgi model (ACG-model, (de)constructing dimensions model), whose main characters are that extra-dimensional space-time are generated dynamically from a four-dimensional gauge theory and that extra dimensions are lattices, will be given first. Then after a concise review of NCG on cyclic groups, actions for gauge fields along extra dimensions will be constructed by virtue of NCG and classical (vacuum) solutions will be solved, with low energy phenomenology being classified accordingly. As a conclusion, the behavior of spontaneous symmetry broken within ACG-model can be determined by noncommutative Yang-Mills theory.