Topologically massive gauge theory: A Lorentzian solution

Abstract

We obtain a Lorentzian solution for the topologically massive non-Abelian gauge theory on AdS space (H) over tilde (3) by means of an SU( 1; 1) gauge transformation of the previously found Abelian solution. There exists a natural scale of length which is determined by the inverse topological mass nu similar to ng(2). In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-) self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an Abelian gauge transformation. Then we present map pi : (H) over tilde (3) -> (H) over tilde (2)(+) including the topological mass which is the Lorentzian analog of the Hopf map. This map yields a global decomposition of (H) over tilde (3) as a trivial (S) over tilde (1) bundle over the upper portion of the pseudosphere (H) over tilde (2)(+) which is the Hyperboloid model for the Lobachevski geometry. This leads to a reduction of the Abelian field equation onto (H) over tilde (2)(+) using a global section of the solution on (H) over tilde (3). Then we discuss the integration of the field equation using the Archimedes map A : (H) over tilde (2)(+) - {N} -> (C) over tilde (2)(P). We also present a brief discussion of the holonomy of the gauge potential and the dual field strength on (H) over tilde (2)(+).