An equivalence of two mass generation mechanisms for gauge fields

Two mass generation mechanisms for gauge theories are studied. It is proved that in the abelian case the topological mass generation mechanism introduced in hep-th/9301060, hep-th/9512216 is equivalent to the mass generation mechanism defined in hep-th/0510240, hep-th/0605050 with the help of ``localization'' of a nonlocal gauge invariant action. In the nonabelian case the former mechanism is known to generate a unitary renormalizable quantum field theory describing a massive vector field.