The dual of non-Abelian Lattice Gauge Theory

Abstract

Non-Abelian Lattice Gauge Theory in Euclidean space-time of dimension d>=2 whose gauge group is any compact Lie group is related to a Spin Foam Model by an exact strong-weak duality transformation. The group degrees of freedom are integrated out and replaced by combinatorial expressions involving irreducible representations and intertwiners of the gauge group. This transformation is available for the partition function, for the expectation value of observables (spin networks), and for the correlator of centre monopoles which is a ratio of partition functions in the original model and an ordinary expectation value in the dual formulation.