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The dual of pure non-Abelian lattice gauge theory as a spin foam model
We derive an exact duality transformation for pure non-Abelian gauge theory
regularized on a lattice. The duality transformation can be applied to gauge
theory with an arbitrary compact Lie group G as the gauge group and on
Euclidean space-time lattices of dimension d >= 2. It maps the partition
function as well as the expectation values of generalized non-Abelian Wilson
loops (spin networks) to expressions involving only finite-dimensional unitary
representations, intertwiners and characters of G. In particular, all group
integrations are explicitly performed. The transformation maps the strong
coupling regime of non-Abelian gauge theory to the weak coupling regime of the
dual model. This dual model is a system in statistical mechanics whose
configurations are spin foams on the lattice.Comment: 28 pages, LaTeX + PicTeX; typographical errors correcte
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