We propose that, in SU(3) gauge theories with fundamental quarks, confinement can be inferred from spectral density of the Dirac operator. This stems from the proposition that its possible behaviors are exhausted by three distinct types (Fig. 1). The monotonic cases are standard and entail confinement with valence chiral symmetry breaking (A) or the lack of both (C,C’). The bimodal (anomalous) option (B) was frequently regarded as an artifact (lattice or other) in previous studies, but we show for the first time that it persists in the continuum limit, and conclude that it informs of a nonconfining phase with broken valence chiral symmetry. This generalization rests on the following. (α) We show that bimodality in Nf = 0 theory past deconfinement temperature Tc is stable with respect to removal of both infrared and ultraviolet cutoffs, indicating that anomalous phase is not an artifact. (β) We demonstrate that transition to bimodality in Nf = 0 is simultaneous with the loss of confinement: anomalous phase occurs for Tc < T < Tch, where Tch is the valence chiral restoration temperature. (γ) Evidence is presented for thermal anomalous phase in Nf = 2 + 1 QCD at physical quark masses, whose onset too coincides with the conventional “crossover Tc.” We conclude that the anomalous regime Tc < T < Tch is very likely a feature of nature’s strong interactions. (δ) Our past studies of zero-temperature Nf + 12 theories revealed that bimodality also arises via purely light-quark effects. As a result, we expect to encounter the anomalous phase on generic paths to valence chiral restoration. . . .
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A. A. is supported by U.S. National Science Foundation under CAREER Grant No. PHY-1151648. I. H. acknowledges the support by Department of Anesthesiology at the University of Kentucky.
Alexandru, Andrei and Horváth, Ivan, "Phases of SU(3) Gauge Theories with Fundamental Quarks via Dirac Spectral Density" (2015). Anesthesiology Faculty Publications. Paper 6.