Spontaneous Symmetry Broken Condition in (De)Constructing Dimensions from Noncommutative Geometry

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.