We study the physics of quark deconfinement on domain walls in four-dimensional supersymmetric SU (N ) Yang-Mills theory, compactified on a small circle with supersymmetric boundary conditions. We numerically examine the properties of BPS domain walls connecting vacua k units apart. We also determine their electric fluxes and use the results to show that Wilson loops of any nonzero N -ality exhibit perimeter law on all k-walls. Our results confirm and extend, to all N and k, the validity of the semiclassical picture of deconfinement of Anber, Sulejmanpasic and one of us (EP), arXiv:1501.06773, providing a microscopic explanation of mixed 0-form/1-form anomaly inflow. arXiv:1909.10979v3 [hep-th] 3 Dec 2019 7 Another property of Wilson loops on DWs with an R 3 worldvolume, i.e. in the R 4 theory, namely their nontrivial braiding (discussed e.g. in [38,46]), cannot be seen in the small-L setup of this paper, as the quarks' worldlines would have to cross.8 Stemming from the results of [19], as explained in EP's talk at Continuous Advances in QCD-2016, see https://conservancy.umn.edu/handle/11299/180346. 9 We have in mind objects composed of N heavy (of mass M Λ) quarks, approaching the static spectator limit (the color flux picture of Fig. 2a may be of relevance for excited dynamical baryons). ∆ vs. Y baryons in lattice QCD, also including light dynamical quarks, are discussed in [47]. 10 In historical order, see [1,2] and the instanton calculation of [3,4] (completed recently in [8,61]).

We study four-dimensional gauge theories with arbitrary simple gauge group with 1-form global center symmetry and 0-form parity or discrete chiral symmetry. We canonically quantize on 𝕋3, in a fixed background field gauging the 1-form symmetry. We show that the mixed 0-form/1-form ’t Hooft anomaly results in a central extension of the global-symmetry operator algebra. We determine this algebra in each case and show that the anomaly implies degeneracies in the spectrum of the Hamiltonian at any finite- size torus. We discuss the consistency of these constraints with both older and recent semiclassical calculations in SU(N) theories, with or without adjoint fermions, as well as with their conjectured infrared phases.