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We discuss recent developments for exact reformulations of lattice fieldtheories in terms of worldlines and worldsheets. In particular we focus on astrategy which is applicable also to non-abelian theories: traces andmatrix/vector products are written as explicit sums over color indices and adual variable is introduced for each individual term. These dual variablescorrespond to fluxes in both, space-time and color for matter fields (Abeliancolor fluxes), or to fluxes in color space around space-time plaquettes forgauge fields (Abelian color cycles). Subsequently all original degrees offreedom, i.e., matter fields and gauge links, can be integrated out.Integrating over complex phases of matter fields gives rise to constraints thatenforce conservation of matter flux on all sites. Integrating out phases ofgauge fields enforces vanishing combined flux of matter- and gauge degrees offreedom. The constraints give rise to a system of worldlines and worldsheets.Integrating over the factors that are not phases (e.g., radial degrees offreedom or contributions from the Haar measure) generates additional weightfactors that together with the constraints implement the full symmetry of theconventional formulation, now in the language of worldlines and worldsheets. Wediscuss the Abelian color flux and Abelian color cycle strategies for threeexamples: the SU(2) principal chiral model with chemical potential coupled totwo of the Noether charges, SU(2) lattice gauge theory coupled to staggeredfermions, as well as full lattice QCD with staggered fermions. For theprincipal chiral model we present some simulation results that illustrateproperties of the worldline dynamics at finite chemical potentials.

Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles