AI 中文总结
该研究针对单连通简单李群上的WZW模型，补全了其定域化公式的缺失因子，关联了定域化结果与阿贝尔理论的格点描述，并在点粒子极限下重现了Frenkel的热核迹线公式。
AI 中文摘要
我们研究紧致、连通且单连通简单李群上圆环的Wess-Zumino-Witten（WZW）模型配分函数的定域化公式。我们找到了Murthy和Witten原始定域化处理中缺失的因子，并证明其与哈密顿形式得到的结果一致。我们追溯其起源至Wess-Zumino振幅的阿贝尔化，该振幅在与极大环面相关的Narain格点CFT中简化为平坦的Kalb-Ramond B场和乐。这建立了定域化结果与对应阿贝尔理论格点描述的直接关联。我们进一步分析圆环配分函数的点粒子极限，其中WZW模型简化为群流形上的量子力学，并重现了Frenkel的热核迹线公式。
英文摘要
We study the localization formula for the partition function of the Wess--Zumino--Witten (WZW) model on the torus for compact, connected, and simply connected simple Lie groups. We identify a missing factor in the original localization treatment of Murthy and Witten and show that it agrees with the result obtained from the Hamiltonian formulation. We trace its origin to the abelianization of the Wess--Zumino amplitude, which reduces to a flat Kalb--Ramond B--field holonomy in a Narain lattice CFT associated with the maximal torus. This establishes a direct relation between the localization result and the lattice description of the corresponding abelian theory. We further analyze the point--particle limit of the torus partition function, in which the WZW model reduces to quantum mechanics on the group manifold, and reproduce Frenkel's heat--kernel trace formula.
