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Linear confinement with Casimir scaling of the string tension in confining gauge theories is a consequence of a certain property of the Polyakov loop related to random matrices. This mechanism does not depend on the details of the theories (neither the gauge group nor dimensions) and explains approximate Casimir scaling below string-breaking length. In this paper, we study 3d SU(2) pure Yang-Mills theory numerically and find the same random-matrix behavior for rectangular Wilson loops. We conjecture that this is a universal feature of strongly coupled confining gauge theories., Comment: 23 pages, 12 figures

We consider the partially-deconfined saddle of large-$N$ pure Yang-Mills theory lying between confined and deconfined phases, in which the color degrees of freedom split into confined and deconfined sectors. Based on the microscopic mechanism of deconfinement, we argue that a flux tube is formed in the confined sector and a linear confinement potential is generated. The string tension should not depend on the size of the confined sector. We provide evidence by studying the finite-temperature strong-coupling lattice gauge theory. In particular, we make analytic predictions assuming linear confinement in the confined sector, and then confirm these by numerical simulations. We discuss some implications of the conjecture to QCD and holography., Comment: A version accepted for publication in JHEP

In gauge theories, spontaneous breaking of the centre symmetry provides a precise definition of deconfinement. In large-$N$ gauge theories, evidence has emerged recently that between confined and deconfined phases a partially-deconfined phase can appear, in which only a subset of colours deconfine. In the partially-deconfined phase, the centre symmetry is spontaneously broken, raising the question of whether an order parameter exists that can distinguish completely- and partially-deconfined phases. We present two examples in gauge theories of global symmetries that are spontaneously broken in the confined phase and preserved in the deconfined phase, and we show that this symmetry is spontaneously broken in the partially-deconfined phase. As a result, in these theories the transition from complete to partial deconfinement is accompanied by the spontaneous breaking of a global symmetry. The two examples are CP symmetry in $\mathcal{N}=1$ super-Yang-Mills with a massive gluino and theta-angle $\theta=\pi$, and chiral symmetry in a strongly-coupled lattice gauge theory. For $\mathcal{N}=1$ SYM we also present numerical evidence that the same phenomenon occurs at finite $N \geq 30$. We thus conjecture that global symmetries may provide order parameters to distinguish completely and partially deconfined phases generically, including at finite $N$., Comment: 42 pages + 2 appendices, 37 figure files in 18 figures