TOPOLOGICAL MASS GENERATION IN 3+1 DIMENSIONS

Abstract

The 4-dimensional theory of a 1-form Abelian gauge field A coupled to a 2-form (antisymmetric tensor) potential B is studied. The two gauge invariances of the theory admit a coupling mB ∧ F where F is the field strength (F=dA) of A. It is shown that this theory is a unitary, renormalizable theory of a massive spin-one field with no additional degrees of freedom. In this sense, it is a generalization to four dimensions of topological mechanisms in two dimensions (the Schwinger model) and three dimensions (Chern-Simons theory). The issue of spontaneous symmetry breaking is also examined.