Topological Sectors of Spin 1 Theories} in 2+1 Dimensions}

TL;DR

This paper investigates the global topological differences between the Topological Massive and Self-dual theories in 2+1 dimensions, revealing how their partition functions differ by a topological factor related to Chern-Simons theory.

Contribution

It introduces a new covariant, first-order gauge action that generalizes the Self-dual action and proves its global equivalence to the Topological Massive gauge theory.

Findings

Partition functions differ by a topological factor

New covariant gauge action generalizes Self-dual theory

Global equivalence between the new action and Topological Massive theory

Abstract

It is shown that the Topological Massive and ``Self-dual'' theories, which are known to provide locally equivalent descriptions of spin 1 theories in 2+1 dimensions, have different global properties when formulated over topologically non-trivial regions of space-time. The partition function of these theories, when constructed on an arbitrary Riemannian manifold, differ by a topological factor, which is equal to the partition function of the pure Chern-Simons theory. This factor is related to the space of solutions of the field equations of the Topological Massive Theory for which the connection is asymptotically flat but not gauge equivalent to zero. A new covariant, first order, gauge action,which generalize 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.