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 gau ge theory with an arbitrary compact Lie group G as the gauge group and on E uclidean space-time lattices of dimension d greater than or equal to 2. It maps the partition function as well as the expectation values of generalize d non-Abelian Wilson loops (spin networks) to expressions involving only fi nite-dimensional unitary representations, intertwiners and characters of G. In particular, all group integrations are explicitly performed. The transf ormation 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 sta tistical mechanics whose configurations are spin foams on the lattice. (C) 2001 Elsevier Science B.V. All rights reserved.