Topological Mass Generation in 3+1 Dimensions

The four-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. † Email Addresses : tjallen, bowick and [email protected]