Localized Modes in the IR Phase of QCD
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916086540140544 |
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| author | Alexandru, Andrei Horváth, Ivan Bhattacharyya, Neel |
| author_facet | Alexandru, Andrei Horváth, Ivan Bhattacharyya, Neel |
| contents | Infrared (IR) dimension function $d_\text{IR}(λ)$ characterizes the space effectively utilized by QCD quarks at Dirac scale $λ$, and indirectly the space occupied by glue fields. It was proposed that its non-analytic behavior in thermal infrared phase reflects the separation of QCD system into an IR component and an independent bulk. Here we study the ``plateau modes" in IR component, whose dimensional properties were puzzling. Indeeed, in the recent metal-to-critical scenario of transition to IR phase, this low-dimensional plateau connects the Anderson-like mobility edge $λ_\text{IR}=0$ in Dirac spectrum with mobility edges $\pm λ_\text{A}$. For this structure to be truly Anderson-like, plateau modes have to be exponentially localized, implying that both the effective distances $L_\text{eff} \propto L^γ$ and the effective volumes $V_\text{eff} \propto L^{d_\text{IR}}$ in these modes grow slower than any positive power of IR cutoff $L$. Although $γ=0$ was confirmed in the plateau, it was found that $d_\text{IR}\approx 1$. Here we apply the recently proposed multidimension technique to the problem. We conclude that a plateau mode of pure-glue QCD at UV cutoff $a \!=\! 0.085\,$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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03621 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Localized Modes in the IR Phase of QCD Alexandru, Andrei Horváth, Ivan Bhattacharyya, Neel High Energy Physics - Lattice High Energy Physics - Theory Nuclear Theory Infrared (IR) dimension function $d_\text{IR}(λ)$ characterizes the space effectively utilized by QCD quarks at Dirac scale $λ$, and indirectly the space occupied by glue fields. It was proposed that its non-analytic behavior in thermal infrared phase reflects the separation of QCD system into an IR component and an independent bulk. Here we study the ``plateau modes" in IR component, whose dimensional properties were puzzling. Indeeed, in the recent metal-to-critical scenario of transition to IR phase, this low-dimensional plateau connects the Anderson-like mobility edge $λ_\text{IR}=0$ in Dirac spectrum with mobility edges $\pm λ_\text{A}$. For this structure to be truly Anderson-like, plateau modes have to be exponentially localized, implying that both the effective distances $L_\text{eff} \propto L^γ$ and the effective volumes $V_\text{eff} \propto L^{d_\text{IR}}$ in these modes grow slower than any positive power of IR cutoff $L$. Although $γ=0$ was confirmed in the plateau, it was found that $d_\text{IR}\approx 1$. Here we apply the recently proposed multidimension technique to the problem. We conclude that a plateau mode of pure-glue QCD at UV cutoff $a \!=\! 0.085\,$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. |
| title | Localized Modes in the IR Phase of QCD |
| topic | High Energy Physics - Lattice High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2310.03621 |