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Zp charged branes in flux compactifications

We consider 4d string compactifications in the presence of fluxes, and classify particles, strings and domain walls arising from wrapped branes which have charges conserved modulo an integer p, and whose annihilation is catalized by fluxes, through the Freed-Witten anomaly or its dual versions. The Z_p-valued strings and particles are associated to Z_p discrete gauge symmetries, which we show are realized as discrete subgroups of 4d U(1) symmetries broken by their Chern-Simons couplings to the background fluxes. We also describe examples where the discrete gauge symmetry group is actually non-Abelian. The Z_p-valued domain walls separate vacua which have different flux quanta, yet are actually equivalent by an integer shift of axion fields (or further string duality symmetries). We argue that certain examples are related by T-duality to the realization of discrete gauge symmetries and Z_p charges from torsion (co)homology. At a formal level, the groups classifying these discrete charges should correspond to a generalization of K-theory in the presence of general fluxes (and including fundamental strings and NS5-branes).