Phases ofSU(3)gauge theories with fundamental quarks via Dirac spectral density

Abstract

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 non-confining phase with broken valence chiral symmetry. This generalization rests on the following. (α) We show that bimodality in N f =0 theory past deconfinement temperature T c 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 N f =0 is simultaneous with the loss of confinement: anomalous phase occurs for T c < T < T ch , where T ch is the valence chiral restoration temperature. (γ) Evidence is presented for thermal anomalous phase in N f =2+1 QCD at physical quark masses, whose onset too coincides with the conventional "crossover T c ". We conclude that the anomalous regime T c < T < T ch is very likely a feature of nature's strong interactions. (δ) Our past studies of zero-temperature N f =12 theories revealed that bimodality also arises via purely light-quark effects. As a result, we expect to encounter anomalous phase on generic paths to valence chiral restoration. We predict its existence also for N f massless flavors (T = 0) in the range N c f < N f < N ch f , where N c f could be quite low. Conventional arguments would associate N ch f with the onset of conformal window.

Possible new phase of thermal QCD

“…[19], a peak at the infrared end of Euclidean Dirac spectral density has been observed in pgQCD above T c . Only recently it was shown [14] that this feature is not a regularization artifact. Here we present evidence that ρ(λ) ∝ λ −1 in IR which, together with ρ(λ) ∝ λ 3 in UV, generates a bimodal structure facilitating scale invariance at both ends of the spectrum.…”

“…In addition, T UV coincides with temperature T ch postulated in Refs. [12][13][14]. The analog of T A has not appeared in the context of pgQCD.…”

“…Due to its crossover nature, the definition of T A is not unique and a suitable choice depends on detailed behavior of λ m (T ). Temperature T A splits B phase into the low T regime B 0 and the B A regime referred to as anomalous [14].…”

“…In Refs. [13,14,21,22] it was found that small mass dynamics at N f = 12, believed by most researchers to be near-conformal, generates the pattern of IR-UV separation closely mimicking that of QCD in IR phase. While originally interpreted as indicating an unexpectedly large In more detail, the sequence…”

“…At asymptotically small m, the running stops at dynamically generated Λ IR > 0, and scale invariance ensues at larger distances: the interacting fixed point entirely runs the IR, whilethe Gaussian one governs UV. The evidence of Refs [13,14,21,22]. suggests that Banks-Zaks fixed point turns on in a sudden manner by theory entering the IR phase (m < m IR ) in mass.…”