发表机构
University of Science and Technology of China; Peng Huanwu Center for Fundamental Theory（中国科学技术大学; 彭桓武基础理论中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究带角势的大N向量模型单态扇区，计算自由能并发现温度与角势满足特定关系时发生Gross-Witten-Wadia相变，角势可调谐相变，无间隙相自由能出现双极点。
AI 中文摘要
我们研究了在角势$\Omega$存在下，$S^1_\beta\times S^2_r$上的大$N$、$O(N)$矢量模型的单态扇区。我们计算了该模型在自由不动点以及非平凡不动点处的自由能。当温度$T$和角势满足关系$T^2r^2\sim N (1-\omega^2)$时，模型发生相变，其中$\omega=r\Omega$，$r$是$S^2$的半径，且$Tr\gg1$，在两个不动点处均发生相变，但数值系数不同。该相变在零角势、$Tr\sim \sqrt{N}$处曾被研究过。在相变以下，完整圆上的全纯特征值分布，在相变以上出现间隙，称为Gross-Witten-Wadia相变。角势为此类相变引入了一个额外参数，通过调节该参数，相变甚至可以在固定温度下发生。我们表明，对于自由模型，相变可以在$1-\omega^2\sim 1/N$时发生，而$Tr\sim O(1)$。对于相互作用模型，计算在极限$Tr\gg1$下进行，因此我们展示了在较大但固定的温度下（该温度不随$\sqrt{N}$缩放）的相同行为。在无间隙相中，自由能在$\omega^2=1$附近对两个不动点均表现出双极点。这可能是因为投影到单态上的理论是非局域的，因此不必遵循局域热有效作用量的主导单极点缩放。
英文摘要
We study the singlet sector of large-$N$, $O(N)$ vector model on $S^1_β\times S^2_r$ in presence of an angular potential $Ω$. We compute the free energy of the model both at the free fixed point as well as the non-trivial fixed point. The model undergoes a phase transition when the temperature $T$ and angular potential attain the relation $T^2r^2\sim N (1-ω^2)$, where $ω=rΩ$ and $r$ is the radius of $S^2$, with $Tr\gg1$, at both the fixed points, with different numerical coefficients. The transition was studied earlier at zero angular potential at $Tr\sim \sqrt{N}$. The holonomy eigenvalue distribution, having support on the full circle below the transition, develops a gap above it, called the Gross-Witten-Wadia transition. The angular potential introduces an additional parameter to such a transition, tuning it, the transition can occur even at a fixed temperature. We show that for the free model transition can occur as $1-ω^2\sim 1/N$ while $Tr\sim O(1)$. For the interacting model the computation is performed at a limit $Tr\gg1$, thus we show the same at a large but fixed temperature which does not scale as $\sqrt{N}$. In the ungapped phase, the free energy exhibits a double pole near $ω^2=1$ for both the fixed points. This is possibly due to the fact that the theory projected onto the singlets is non-local and therefore need not obey the leading simple pole scaling of a local thermal effective action.
Comments41 pages, 1 figure
