The "Dual" Variables Of Yang-Mills Theory And Local Gauge Invariant Variables

Details The "Dual" Variables Of Yang-Mills Theory And Local Gauge Invariant Variables The "Dual" Variables Of Yang-Mills Theory And Local Gauge Invariant Variables

1995-07-06

arxiv.org/abs/hep-th/9507036v3

Int.J.Mod.Phys. A11 (1996) 5701-5728

Physics

High Energy Physics

High Energy Physics - Theory

34pp, LaTeX, Corrections in references

Scientific paper

10.1142/S0217751X96002625

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 $\alpha_s$. 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.

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