Localized modes in the IR phase of QCD

Journal Article · 02 January 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.109.014501 · OSTI ID:2274981

Alexandru, Andrei; Horváth, Ivan ; Bhattacharyya, Neel

Infrared (IR) dimension function $d_{\mathrm{IR}}\left(\lambda \right)$ characterizes the space effectively utilized by QCD quarks at Dirac scale $\lambda$ , and indirectly the space occupied by glue fields. It was proposed that its nonanalytic behavior in thermal reflects the separation of QCD system into an IR component and an independent bulk. Here we study the “plateau modes” in the IR component, whose dimensional properties were puzzling. Indeed, in the recent scenario of transition to IR phase, this low-dimensional plateau connects the Anderson-like mobility edge ${\lambda }_{\mathrm{IR}}=0$ in Dirac spectrum with mobility edges $\pm {\lambda }_{\mathrm{A}}$ . For this structure to be truly Anderson-like, plateau modes have to be exponentially localized, implying that both the effective distances $L_{\mathrm{eff}}\propto L^{\gamma }$ and the effective volumes $V_{\mathrm{eff}}\propto L^{d_{\mathrm{IR}}}$ in these modes grow slower than any positive power of IR cutoff $L$ . Although $\gamma =0$ was confirmed in the plateau, it was found that $d_{\mathrm{IR}}\approx 1$ . Here we apply the recently proposed technique to the problem. We conclude that a plateau mode of pure-glue QCD at UV cutoff $a=0.085\mathrm{fm}$ occupies a subvolume of IR dimension zero with probability at least 0.9999, substantiating this aspect of metal-to-critical scenario to a respective degree. Published by the American Physical Society 2024

• Research Organization: George Washington Univ., Washington, DC (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC)
• Grant/Contract Number: FG02-95ER40907
• OSTI ID: 2274981
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 1 Vol. 109; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English