AI 中文总结
研究大N时非阿贝尔 Thirring 模型，通过计算电流和复合电流算符两点关联函数到\(\lambda\)三次方阶，提取\(\beta\)函数和反常维度，发现不存在特定阶数的额外临界点，结果与部分研究一致，与另一说法矛盾。
AI 中文摘要
我们考虑具有变形参数\(\lambda\)、处于等级\(k\)的半单群\(G\)的非阿贝尔玻色化 Thirring 模型。假设群\(G\)在伴随表示中的二次卡西米尔\(c_G\)值很大，我们计算电流和复合电流算符的两点关联函数到\(\lambda\)的三次方阶。由此提取\(\beta\)函数以及电流和复合电流算符的反常维度，表明不存在阶数为\(k/c_G\)的额外临界点。我们的发现与费米子非阿贝尔 Thirring 模型中 Destri 和 de Vega 的结果一致，但与 Dashen 和 Frishman 关于存在阶数为\(1/c_G\)的额外不动点的说法相矛盾。
英文摘要
We consider the non-Abelian bosonized Thirring model for a semi-simple group $G$ at level $k$, with deformation parameter $λ$. We compute the two-point correlation functions of current and composite current operators to cubic order in $λ$, assuming large values of the quadratic Casimir $c_G$ of the group $G$ in the adjoint representation. From these, we extract the $β$-function and the anomalous dimensions of both the current and composite current operators, showing the absence of an additional critical point of order $k/c_G$. Our findings align with those of Destri & de Vega for the Fermionic non-Abelian Thirring model, but contradict the claim in Dashen & Frishman regarding the existence of an additional fixed point of order $1/c_G$.
Commentsv1: Latex, 1+38 pages
