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We propose a new approach to strong coupling series and dual representationsfor non-abelian lattice gauge theories using the SU(2) case as an example. TheWilson gauge action is written as a sum over "abelian color cycles" (ACC) whichcorrespond to loops in color space around plaquettes. The ACCs are complexnumbers which can be commuted freely such that the strong coupling series andthe dual representation can be obtained as in the abelian case. Using asuitable representation of the SU(2) gauge variables we integrate out alloriginal gauge links and identify the constraints for the dual variables in theSU(2) case. We show that the construction can be generalized to the case ofSU(2) gauge fields with staggered fermions. The result is a strong couplingseries where all gauge integrals are known in closed form and we discuss itsapplicability for possible dual simulations. The abelian color cycle conceptcan be generalized to other non-abelian gauge groups such as SU(3).

Abelian color cycles: a new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theory