The dual of pure nonAbelian lattice gauge theory as a spin foam model
Abstract
We derive an exact duality transformation for pure nonAbelian 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 spacetime lattices of dimension d⩾2. It maps the partition function as well as the expectation values of generalized nonAbelian Wilson loops (spin networks) to expressions involving only finitedimensional unitary representations, intertwiners and characters of G. In particular, all group integrations are explicitly performed. The transformation maps the strong coupling regime of nonAbelian 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.
 Publication:

Nuclear Physics B
 Pub Date:
 March 2001
 DOI:
 10.1016/S05503213(00)007707
 arXiv:
 arXiv:hepth/0008095
 Bibcode:
 2001NuPhB.598..400O
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Lattice
 EPrint:
 28 pages, LaTeX + PicTeX