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Earlier, two of us and M. Unsal [arXiv:1112.6389] showed that some 4d gaugetheories, compactified on a small spatial circle of size L and considered attemperatures 1/beta near deconfinement, are dual to 2d "affine" XY-spin models.We use the duality to study deconfinement in SU(3)/Z_3 theories with n_f>1massless adjoint Weyl fermions, QCD(adj) on R^2 x S^1_beta x S^1_L. The"affine"XY-model describes two "spins" - compact scalars taking values in the SU(3)root lattice, with nearest-neighbor interactions and subject to an "externalfield" preserving the topological Z_3^t and a discrete Z_3^chi subgroup of thechiral symmetry of the 4d gauge theory. The equivalent Coulomb gasrepresentation of the theory exhibits electric-magnetic duality, which is alsoa high-/low-temperature duality. A renormalization group analysis suggests -but is not convincing, due to the onset of strong coupling - that the self-dualpoint is a fixed point, implying a continuous deconfinement transition. Here,we study the nature of the transition via Monte Carlo simulations. The Z_3^t xZ_3^chi order parameter, its susceptibility, the vortex density, the energy perspin, and the specific heat are measured over a range of volumes, temperatures,and "external field" strengths (in the gauge theory, these correspond tomagnetic bion fugacities). The finite-size scaling of the susceptibility andspecific heat we find is characteristic of a first-order transition.Furthermore, for sufficiently large but still smaller than unity bion fugacity(as can be achieved upon an increase of the S^1_L size), at the criticaltemperature we find two distinct peaks of the energy probability distribution,indicative of a first-order transition, as has been seen in earlier simulationsof the full 4d QCD(adj) theory. We end with discussions of the global phasediagram in the beta-L plane for different numbers of flavors.

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