A new class of rank breaking orbifolds

We describe field-theory T2/Zn orbifolds that offer new ways of breaking SU(N) to lower rank subgroups. We introduce a novel way of embedding the point group into the gauge group, beyond the usual mapping of torus and root lattices. For this mechanism to work the torus Wilson lines must carry nontrivial 't Hooft flux. The rank lowering mechanism proceeds by inner automorphisms but is not related to continuous Wilson lines and does not give rise to any associated moduli. We give a complete classification of all possible SU(N) breaking patterns. We also show that the case of general gauge group can already be understood entirely in terms of the SU(N) case and the knowledge of standard orbifold constructions with vanishing 't Hooft flux.