The hypothesis that the QCD vacuum can be modeled as a dual superconductor is a powerful tool to describe the distribution of the color field generated by a quark-antiquark static pair and, as such, can provide useful clues for the understanding of confinement. In this work we investigate, by lattice Monte Carlo simulations of the SU (3) pure gauge theory and of (2+1)-flavor QCD with physical mass settings, some properties of the chromoelectric flux tube at zero temperature and their dependence on the physical distance between the static sources. We draw some conclusions about the validity domain of the dual superconductor picture.

Attempts to extract the order of the chiral transition of QCD at zero chemical potential, with two dynamical flavors of massless quarks, from simulations with progressively decreasing pion mass, have remained inconclusive because of their increasing numerical cost. In an alternative approach to this problem, we consider the path integral as a function of continuous number N f of degenerate quarks. If the transition in the chiral limit is first order for N f ≥ 3, a second-order transition for N f ¼ 2 then requires a tricritical point in between. This, in turn, implies tricritical scaling of the critical boundary line between the first-order and crossover regions as the chiral limit is approached. Noninteger numbers of fermion flavors are easily implemented within the staggered fermion discretization. Exploratory simulations at μ ¼ 0 and N f ¼ 2.8, 2.6, 2.4, 2.2, 2.1, on coarse N τ ¼ 4 lattices, indeed show a smooth variation of the critical mass mapping out a critical line in the (m, N f ) plane. For the smallest masses, the line appears consistent with tricritical scaling, allowing for an extrapolation to the chiral limit.

The nature of the QCD chiral phase transition in the limit of vanishing quark masses has remained elusive for a long time, since it cannot be simulated directly on the lattice and is strongly cutoff-dependent. We report on a comprehensive ongoing study using unimproved staggered fermions with Nf ∈ [2, 8] mass-degenerate flavours on Nτ ∈ {4, 6, 8} lattices, in which we locate the chiral critical surface separating regions with first-order transitions from crossover regions in the bare parameter space of the lattice theory. Employing the fact that it terminates in a tricritical line, this surface can be extrapolated to the chiral limit using tricritical scaling with known exponents. Knowing the order of the transitions in the lattice parameter space, conclusions for approaching the continuum chiral limit in the proper order can be drawn. While a narrow first-order region cannot be ruled out, we find initial evidence consistent with a second-order chiral transition in all massless theories with Nf ≤ 6, and possibly up to the onset of the conformal window at 9 ≲ $$ {N}_{\mathrm{f}}^{\ast } $$ N f ∗ ≲ 12. A reanalysis of already published $$ \mathcal{O} $$ O (a)-improved Nf = 3 Wilson data on Nτ ∈ [4, 12] is also consistent with tricritical scaling, and the associated change from first to second-order on the way to the continuum chiral limit. We discuss a modified Columbia plot and a phase diagram for many-flavour QCD that reflect these possible features.

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We extend a previous numerical study of SU(3) Yang-Mills theory in which we measured the spatial distribution of all components of the color fields surrounding a static quark-antiquark pair for a wide range of quarkantiquark separations, and provided evidence that the simulated gauge invariant chromoelectric field can be separated into a Coulomb-like 'perturbative' field and a 'nonperturbative' field, identified as the confining part of the SU(3) flux tube field.In this paper we hypothesize that the fluctuating color fields not measured in our simulations do not contribute to the string tension. Under this assumption the string tension is determined by the color fields we measure, which form a tensor F µν pointing in a single direction in color space. We call this the Maxwell mechanism of confinement.We provide an additional procedure to isolate the nonperturbative (confining) field. We then extract the string tension from a stress energy-momentum tensor T µν having the Maxwell form, constructed from the non-perturbative part of the tensor F µν obtained from our simulations.To test our hypothesis we calculate the string tension from our simulations of the color fields for ten values of the quark-antiquark separation ranging from 0.37 fm to 1.2 fm. We also calculate the spatial distributions of the energymomentum tensor T µν surrounding static quarks for this range of separations, and we compare these distributions with those obtained from direct simulations of the energymomentum tensor in SU(3) Yang-Mills theory. a