强耦合QCD中的谱求和规则与相变
Spectral sum rules and phase transition in strongly coupled QCD
AI总结：
本文通过同时考虑色电和色磁尺度建立强耦合QCD夸克谱求和规则，发现谱函数具有二维复能量非解析贡献，并揭示由磁尺度诱导的、以热质量为序参量的QCD内禀相变，为退禁闭机制提供新见解。
摘要：
通过纳入（色）电尺度 $gT$ 和（色）磁尺度 $g^2T$ 的贡献，我们为强耦合QCD建立了满足量子力学所要求的费米-狄拉克统计的夸克谱求和规则。与QED和弱耦合QCD的谱函数由实能量 $p_0 \in \mathbb{R}$ 上的不连续零维（极点）和一维（分支割线）非解析贡献组成形成鲜明对比，推导出的强耦合夸克谱函数具有来自复能量 $p_0 \in \mathbb{C}$ 的连续但非解析的贡献，其本质上是二维的。根据新的求和规则，我们揭示了QCD在小耦合下的三模式相与大耦合下的单模式相之间存在一个内禀相变。该相变由磁尺度诱导，磁尺度产生一个无质量的类流体力学模式，该模式具有真正的非阿贝尔特征，即正定性破坏，并作为洛伦兹对称性破缺的戈德斯通模式。热质量作为该相变的序参量，在大耦合下消失，这与来自Dyson-Schwinger方程和规范/引力对偶的唯象预言一致。这一结果为QCD退禁闭相变的机制提供了新的见解。
英文摘要：
By incorporating contributions from both the (chromo)electric scale $gT$ and (chromo)magnetic scale $g^2T$, we establish spectral sum rules of quarks for strongly coupled QCD that respect Fermi-Dirac statistics as required by quantum mechanics. In sharp contrast to QED and weakly coupled QCD whose spectral functions consist of discontinuous zero-dimensional (poles) and one-dimensional (branch cuts) non-analytic contributions from real energy $p_0 \in \mathbb{R}$, the derived spectral function for strongly coupled quarks features continuous but non-analytic contributions from complex energy $p_0 \in \mathbb{C}$ that are two-dimensional in nature. In light of the novel sum rules, we uncover an intrinsic QCD transition between a three-mode phase at small coupling and a one-mode phase at large coupling. The transition is induced by the magnetic scale that generates a massless hydro-like mode with the genuine non-Abelian feature of positivity violation and serving as the Goldstone mode of the Lorentz symmetry breaking. The thermal mass serves as an order parameter of the transition and vanishes at large coupling in line with phenomenological predictions from Dyson-Schwinger equations and gauge/gravity duality. This result provides novel insights into the mechanism of the QCD deconfinement transition.
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