Higher Chern-Simons-Antoniadis-Savvidy forms based on crossed modules

Abstract: We present higher Chern-Simons-Antoniadis-Savvidy (ChSAS) forms based on crossed modules. We start from introducing a generalized multilineal symmetric invariant polynomial for the differential crossed modules and constructing a metric independent, higher gauge invariant, and closed form using the higher curvature forms. Then, we establish the higher Chern-Weil theorem and prove that the higher ChSAS forms is a special case of this theorem. Finally, we get the link of two independent higher ChSAS theories.