Higgs Mechanism with a Topological Term

In cases of both abelian and nonabelian gauge groups, we consider the Higgs mechanism in topologically massive gauge theories in an arbitrary space-time dimension. It is shown that the presence of a topological term makes it possible to shift mass of gauge fields in a nontrivial way compared to the conventional value at the classical tree level. We correct the previous misleading statement with respect to the counting of physical degrees of freedom, where it is shown that gauge fields become massive by 'eating' the Nambu-Goldstone boson and a higher-rank tensor field, but a new massless scalar appears in the spectrum so the number of the physical degrees of freedom remains unchanged before and after the spontaneous symmetry breakdown. Some related phenomenological implications and applications to superstring theory are briefly commented.