Equivalence of the Self-Dual Model and Maxwell-Chern-Simons Theory on Arbitrary Manifolds

TL;DR

This paper demonstrates the equivalence between the Self-Dual Model and Maxwell-Chern-Simons theory on arbitrary manifolds by comparing their partition functions, revealing a deep connection influenced by the manifold's geometry.

Contribution

It provides an explicit derivation of the partition functions for both models and shows their ratio matches that of abelian Chern-Simons theory, highlighting a geometric phase factor.

Findings

Partition functions of the Self-Dual Model and Maxwell-Chern-Simons theory are explicitly computed.

The ratio of these partition functions equals that of abelian Chern-Simons theory, up to a geometric phase.

The equivalence holds on arbitrary manifolds, emphasizing topological aspects.

Abstract

Using a group-invariant version of the Faddeev-Popov method we explicitly obtain the partition functions of the Self-Dual Model and Maxwell-Chern-Simons theory. We show that their ratio coincides with the partition function of abelian Chern-Simons theory to within a phase factor depending on the geometrical properties of the manifold.