标题： 二维量子色动力学与可积性，第二部分：广义量子色动力学 显示英文标题

标题： 2d QCD and Integrability, Part II: Generalized QCD

摘要： 我们将大范围的$N_c$QCD$_2$的可积结构和谱的解析性研究扩展到一类称为广义 QCD 的理论，这类理论由与基本表示中的夸克耦合的拉格朗日量$\mathcal{L}\propto {\rm tr}\,B\wedge F- {\rm tr}\,V(B)$给出。 我们将介子谱的 Bethe-Salpeter 方程重新表述为 TQ-Baxter 方程，并为任意给定的多项式$V(B)$以封闭形式确定转移矩阵。 利用相关的 Fredholm 方程，我们数值研究了谱作为$V(B)$系数函数的解析结构。 我们确定了理论允许介子正且离散谱的耦合参数区域。 此外，我们揭示了一个具有无穷多临界点的多叶结构，在该结构中多个介子同时变为无质量。 最后，我们展示了这种结构在具有 SU(2) 规范群的广义 QCD 的大表示极限中仍然存在。 显示英文摘要

摘要： We extend the study of integrable structures and analyticity of the spectrum in large $N_c$ QCD$_2$ to a broad class of theories called the generalized QCD, which are given by the Lagrangian $\mathcal{L}\propto {\rm tr}\,B\wedge F- {\rm tr}\,V(B)$ coupled to quarks in the fundamental representation. We recast the Bethe-Salpeter equation for the meson spectrum into a TQ-Baxter equation and determine a transfer matrix in a closed form for any given polynomial $V(B)$. Using an associated Fredholm equation, we numerically study the analytic structures of the spectrum as a function of the coefficients of $V(B)$. We determine the region of couplings where the theory admits a positive and discrete spectrum of mesons. Furthermore, we uncover a multi-sheeted structure with infinitely many multi-critical points, where several mesons become simultaneously massless. Lastly, we illustrate that this structure persists in the large-representation limit of the generalized QCD with the SU(2) gauge group.