The reduction of five dimensional Chern–Simons theories

The effects of gauge symmetries on Lagrangian gauge theories which include the Chern–Simons term are studied herein. It is found that the Chern–Simons term appended to a five dimensional Yang–Mills theory makes nontrivial contributions to the classical field equations in four and two dimensions depending on the gauge group, but makes no contribution to the field equations in three dimensions, regardless of the gauge group. In addition to the reduction of Yang–Mills–Chern–Simons, the pure Chern-Simons theory is reduced in five dimensions—a topological field theory—to two and three dimensions. The potential physical observability of solutions to the resulting field equations is examined by determining if a nontrivial spontaneous symmetry breaking is permitted.