The ''dual'' variables of Yang-Mills theory and local gauge-invariant variables

After adding auxiliary fields and integrating out the original variables, the Yang-Mills action can be expressed in terms of local gauge-invariant variables. This method reproduces the known solution of the two-dimensional SU(N) theory. In more than two dimensions the action splits into a topological part and a part proportional to cr,. We demonstrate the procedure for SU(2) in three dimensions where we reproduce a gravity-like theory. We discuss the four-dimensional case as well. We use a cubic expression in the fields as a space-time metric to obtain a covariant Lagrangian. We also show how the four-dimensional SU(2) theory can be expressed in terms of a local action with six degrees of freedom only.