TOPOLOGICAL SECTORS OF SPIN-1 THEORIES IN 2-DIMENSIONS(1)

It is shown that the topological massive and ''self-dual'' theories, w hich are known to provide locally equivalent descriptions of spin 1 th eories in 2 + 1 dimensions, have different global properties when form ulated over topologically non-trivial regions of space-time. The parti tion function of these theories, when constructed on an arbitrary Riem annian manifold, differ by a topological factor, which is equal to the partition function of the pure Chern-Simons theory. This factor is re lated to the space of solutions of the field equations of the topologi cal massive theory for which the connection is asymptotically flat but not gauge equivalent to zero. A new covariant, first order, gauge act ion, which generalizes the ''self-dual'' action, is then proposed. It is obtained by sewing local self-dual theories. Its global equivalence to the topological massive gauge theory is shown.