Kramers-Wannier duality with Abelian Color Fluxes for the SU(2) principal chiral model
We derive a full Kramers-Wannier dualization of the SU(2) principal chiral model. In a first step the trace and color multiplications in the action are written explicitly, such that only commuting numbers ("Abelian Color Fluxes") remain. The individual Boltzmann factors are then expanded and the original degrees of freedom are integrated out explicitly. The expansion indices become the new variables which are subject to constraints. We show that after a suitable reorganization of the new variables the constraints can be resolved by switching to the dual lattice. The resulting dual form implements the original symmetries in an interesting geometrical way, which we discuss for the model at different numbers of dimensions.
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