AI 中文总结
该研究通过Artin-Ihara L-函数统一描述图上广义Kazakov-Migdal模型，将圈图上的KM型模型转化为随机分拆模型，求解发现其相变与玻色-爱因斯坦凝聚相关，还建立了酉矩阵本征值密度与随机分拆Maya图密度的关系。
AI 中文摘要
我们通过Artin-Ihara L-函数在图上引入Kazakov-Migdal（KM）型规范理论，对先前工作中提出的模型提供统一描述。利用群流形上的调和分析，我们将圈图上的KM型模型重新表述为受Schur测度支配的随机分拆模型。我们在大Nc极限下，将基础表示中圈图上的KM型模型作为随机分拆模型严格求解，证明当杨图的极限形状触及允许表示空间边界时，Gross-Witten-Wadia相变恰好发生。我们进一步阐明该相变与玻色-爱因斯坦凝聚密切相关，且强弱耦合对偶具有自然的组合解释，即杨图与其补集的交换，这反映了Artin-Ihara L-函数的函数方程。我们还通过从谱曲线推导 droplet 图像，建立了酉矩阵的本征值密度与随机分拆的Maya图密度之间的明确关系。
英文摘要
We introduce Kazakov-Migdal (KM)-type gauge theories on graphs via the Artin-Ihara $L$-function, providing a unified description of the models proposed in prior works. Using harmonic analysis on the group manifold, we reformulate the KM-type model on the cycle graph as a random partition model governed by the Schur measure. We exactly solve the KM-type model on the cycle graph in the fundamental representation as the random partition model in the large $N_c$ limit and demonstrate that the Gross-Witten-Wadia phase transition occurs precisely when the limiting shape of the Young diagram touches the boundary of the allowed representation space. We further clarify that this phase transition is intimately related to Bose-Einstein condensation, and the strong/weak coupling duality possesses a natural combinatorial interpretation as the exchange between the Young diagram and its complement, reflecting the functional equation of the Artin-Ihara $L$-function. We also establish a definitive relationship between the eigenvalue density of the unitary matrix and the Maya diagram density of the random partitions by deriving a droplet picture from the spectral curve.
Comments46 pages, 7 figures, typos corrected
