发表机构
Tata Institute of Fundamental Research（塔塔基础研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究旋转 $S^1\ imes S^2$ 上临界大-$N$ $O(N)$ 模型的热配分函数，通过 Weyl 协变流体静力学展开和近光速极限几何，揭示其半普适行为，并计算理论依赖的修正。
AI 中文摘要
我们研究了旋转 $S^1\ imes S^2$ 上临界大-$N$ $O(N)$ 模型的热配分函数。旋转使得鞍点纬度依赖，其主导轮廓由局域温度决定。利用 Weyl 协变流体静力学展开，我们在高温和半普适极限下确定了四阶导数阶的配分函数。在近光速极限下，赤道附近的几何约化为 pp 波，并捕获了配分函数的预期半普适行为。我们直接在该极限几何上计算了相应的理论依赖留数，分别在高温和低温下进行。高温结果与球面计算的近光速极限一致，而低温展开揭示了由鞍点对热源响应引起的相互作用依赖修正。
英文摘要
We study the thermal partition function of the critical large-$N$ $O(N)$ model on rotating $S^1\times S^2$. Rotation makes the saddle latitude dependent, with its leading profile governed by the local temperature. Using a Weyl-covariant hydrostatic expansion, we determine the partition function through four-derivative order in high-temperature and semi-universal limits. In the near-light-speed limit, the geometry around the equator reduces to a pp-wave and captures the expected semi-universal behavior of the partition function. We compute the corresponding theory-dependent residue directly on this limiting geometry, both at high and low temperatures. The high-temperature result agrees with the near-light-speed limit of the sphere calculation, while the low-temperature expansion reveals interaction-dependent corrections arising from the response of the saddle to the thermal source.
Comments21 pages + appendices
