Journal
NUCLEAR PHYSICS B
Volume 598, Issue 1-2, Pages 400-426Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/S0550-3213(00)00770-7
Keywords
lattice gauge theory; non-Abelian; duality; spin network; spin foam; Wilson loop
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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 greater than or equal to 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. (C) 2001 Elsevier Science B.V. All rights reserved.
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