The dual of pure non-Abelian lattice gauge theory as a spin foam model

Details The dual of pure non-Abelian lattice gauge theory as a spin foam model The dual of pure non-Abelian lattice gauge theory as a spin foam model

2000-08-11

arxiv.org/abs/hep-th/0008095v2

Nucl.Phys.B598:400-426,2001

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, LaTeX + PicTeX; typographical errors corrected

Scientific paper

10.1016/S0550-3213(00)00770-7

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.

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