Yang-Mills theory as a quantum gravity with ``æther''. (Q1873846)

The authors express the pure SU\((N)\) Yang-Mills action in three dimensions and the pure SU\((2)\) Yang-Mills action in four dimensions in terms of local gauge-invariant variables. The basic feature of these variables is that the respective Yang-Mills actions decompose into two terms. One term can be considered as a generalization of the Einstein-Hilbert action and which is invariant with respect to the group of diffeomorphisms. The other term, called the ``æther term'', is not invariant with respect to diffeomorphisms and distinguishes Yang-Mills theory from non-propagating topological BF gravity. Using the path integral procedure the authors show that the original invariance under dual gauge transformations manifests itself as a symmetry under mixing fields with different spins. As \(N\) tends to infinity, an infinite tower of spins are related by symmetry transformations.