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The SU(3)/Z_3 QCD(adj) deconfinement transition via the gauge theory/"affine" XY-model duality

Previously, it was shown that some 4d gauge theories, compactified on a small spatial circle and considered at temperatures near deconfinement, are dual to 2d "affine" XY-spin models. We exploit this duality to study the deconfining phase transition of SU(3)/Z 3 gauge theories with n_f massless adjoint Weyl fermions.  The"affine" XY-model describes two "spins"  scalars taking values in the SU(3) root lattice, with nearest-neighbor interactions and subject to an "external field" preserving the topological Z 3 t and a discrete Z 3 ^chi subgroup of the chiral symmetry of the 4d gauge theory. We study the nature of the transition via Monte Carlo simulations of the dual spin model. Interestingly enough, we find that the transition is a first-order, as has been seen in earlier simulations of the full 4d QCD(adj) theory. This finding, along with others, may open the door into a new paradigm to tackle complicated strong coupling problems.