Abelian Color Cycle approach for the dualization of non-abelian lattice field theories
The Abelian Color Cycle (ACC) technique is a method to dualize non-abelian lattice field theories. The crucial step of this approach is to decompose the action into a sum over complex numbers by writing explicitly all the traces, matrix and vector multiplications. This allows for the factorization of the Boltzmann weight into local factors, that are then Taylor expanded. After the analytical integration of the conventional degrees of freedom the partition function is exactly rewritten in terms of new, so called dual variables. They are color fluxes around plaquettes (ACC) for the gauge degrees of freedom, while the dual variables for the fermion fields form monomers, dimers and loops on the lattice. The new variables have to satisfy color flux constraints that reflect the original gauge symmetry of the theory. The partition function assumes the form of a strong coupling expansion, where all terms are known in closed form. We present the application of this method to pure SU(2) and SU(3) lattice gauge theories, as well as its extension to including staggered fermions.
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