Separation of Infrared and Bulk in Thermal QCD

Abstract: A new thermal regime of QCD, featuring decoupled scale-invariant infrared glue, has been proposed to exist both in pure-glue (N$f$=0) and ``real-world" (N$_f$=2+1 at physical quark masses) QCD. In this {\it IR phase}, elementary degrees of freedom flood the infrared, forming a distinct component independent from the bulk. This behavior necessitates non-analyticities in the theory. In pure-glue QCD, such non-analyticities have been shown to arise via Anderson-like mobility edges in Dirac spectra ($\lambda{\rm IR} !=! 0$, $\pm \lambda_\text{A} !\neq! 0$), as manifested in the dimension function $d_{\rm IR} (\lambda)$. Here, we present the first evidence, based on lattice QCD calculation at $a$=0.105 fm, that this mechanism is also at work in real-world QCD, thus supporting the existence of the proposed IR regime in nature. An important aspect of our results is that, while at $T!=!234\,$MeV we find a dimensional jump between zero modes and lowest near-zero modes very close to unity ($d_{\rm IR} !=!3$ to $d_{\rm IR} !\simeq! 2$), similar to the IR phase of pure-glue QCD, at $T!=!187\,$MeV we observe a continuous $\lambda$-dependence. This suggests that thermal states just {\it above} the chiral crossover are non-analytically (in $T$) connected to thermal state at $T!=!234\,$MeV, supporting the key original proposition that the transition into the IR regime occurs at a temperature strictly above the chiral crossover.