发表机构
Research Center for the Early Universe (RESCEU); Graduate School of Science, The University of Tokyo（早期宇宙研究中心（RESCEU）; 东京大学理学研究生院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明虚转动QCD中角速度决定电荷共轭是否破缺，其破缺角速度集合呈分形结构，且无理角速度对应零温禁闭态。
AI 中文摘要
我们证明，在虚角速度$\Omega_I$旋转的热QCD中，角速度不仅选择体相的温度，还决定电荷共轭$C$是否在那里破缺。对于温度为$T$、虚夸克化学势为$\theta$的QCD，当$\Omega_I/2\pi=p/q$（最简分数）时，远离旋转轴的体相与非旋转QCD在温度$T/q$和虚夸克化学势$\theta'=q\theta+\pi(p+q+1)$下的热平衡态相同；这仅由欧几里得边界条件和局域性得出，且非微扰成立。因此，即使在零夸克化学势下，当$p$和$q$均为奇数时，体相处于Roberge-Weiss（RW）点，且对于$T>qT_{\rm RW}$（$T_{\rm RW}$为RW端点温度），$C$在那里自发破缺。例如，$\Omega_I=2\pi/3$和$4\pi/3$处的体相温度均为$T/3$，但只有前者能破缺$C$。$C$破缺的虚角速度集合具有分形结构：升高$T$会添加分母越来越大的有理数。在无理数$\Omega_I/2\pi$时，体相对应于任意$T$下的零温QCD，并保持禁闭。
英文摘要
We show that in hot QCD rotating at an imaginary angular velocity $Ω_I$, the angular velocity selects not only the temperature of the bulk but whether charge conjugation $C$ is broken there. For QCD at temperature $T$ and imaginary quark chemical potential $θ$, with $Ω_I/2π=p/q$ in lowest terms, the bulk far from the rotation axis is in the same thermal equilibrium state as nonrotating QCD at temperature $T/q$ and imaginary quark chemical potential $θ'=qθ+π(p+q+1)$; this follows from the Euclidean boundary conditions and locality alone, and holds nonperturbatively. Consequently, even at zero quark chemical potential, the bulk is placed at the Roberge-Weiss (RW) point whenever $p$ and $q$ are both odd, and $C$ is spontaneously broken there for $T>qT_{\rm RW}$, with $T_{\rm RW}$ the RW endpoint temperature. The bulks at $Ω_I=2π/3$ and $4π/3$, for example, are both at temperature $T/3$, yet only the former can break $C$. The set of imaginary angular velocities at which $C$ is broken has a fractal structure: raising $T$ adds rationals of ever larger denominator. At irrational $Ω_I/2π$ the bulk corresponds to zero-temperature QCD at any $T$ and remains confined.
Comments6 pages, 2 figures
