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

Abstract

Earlier, two of us and M. Unsal [arXiv:1112.6389] showed that some 4d gauge theories, compactified on a small spatial circle of size L and considered at temperatures 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>1 massless 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 "external field" preserving the topological Z_3^t and a discrete Z_3^chi subgroup of the chiral symmetry of the 4d gauge theory. The equivalent Coulomb gas representation of the theory exhibits electric-magnetic duality, which is also a high-/low-temperature duality. A renormalization group analysis suggests - but is not convincing, due to the onset of strong coupling - that the self-dual point 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 x Z_3^chi order parameter, its susceptibility, the vortex density, the energy per spin, and the specific heat are measured over a range of volumes, temperatures, and "external field" strengths (in the gauge theory, these correspond to magnetic bion fugacities). The finite-size scaling of the susceptibility and specific 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 critical temperature we find two distinct peaks of the energy probability distribution, indicative of a first-order transition, as has been seen in earlier simulations of the full 4d QCD(adj) theory. We end with discussions of the global phase diagram in the beta-L plane for different numbers of flavors.

26 pages, 12 figures

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• (S)QCD on R^3 x S^1: Screening of Polyakov loop by fundamental quarks and the demise of semi-classics
• Deconfinement in N=1 super Yang-Mills theory on R^3 x S^1 via dual-Coulomb gas and "affine" XY-model
• Theta dependence of the deconfining phase transition in pure SU(N_c) Yang-Mills theories
• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
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• Self-conjugate QCD
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• Classification of compactified $su(N_c)$ gauge theories with fermions in all representations
• The abelian confinement mechanism revisited: new aspects of the Georgi-Glashow model
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• Charge-density wave fluctuation driven composite order in the layered Kagome Metals
• Deconfinement on ${\mathbb{R}}^2\times S_L^1\times S_{\beta }^1$ for all gauge groups and duality to double Coulomb Gas
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