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We present a new dual representation for lattice QCD in terms of wordlinesand worldsheets. The exact reformulation is carried out using the recentlydeveloped abelian color flux method where the action is decomposed intocommuting minimal terms that connect different colors on neighboring sites.Expanding the Boltzmann factors for these commuting terms allows one toreorganize the gauge field contributions according to links such that the gaugefields can be integrated out in closed form. The emerging constraints give thedual variables the structure of worldlines for the fermions and worldsheets forthe gauge degrees of freedom. The partition sum has the form of a strongcoupling expansion and with the abelian color flux approach discussed here allcoefficients of the expansion are known in closed form. We present the dualform for three cases: pure SU(3) lattice gauge theory, strong coupling QCD andfull QCD, and discuss in detail the constraints for the color fluxes and theirphysical interpretation.

Dual representation of lattice QCD with worldlines and worldsheets of abelian color fluxes