论文标题
伴随Majoraana QCD $ _2 $在有限$ n $
Adjoint Majorana QCD$_2$ at Finite $N$
论文作者
论文摘要
$ 1+1 $ -Dimensional $ \ mathrm {su}（n）$量规理论与Majoraga fermion耦合在伴随表示中的大型$ n $限制，使用轻单量化进行了研究。在这里，我们将这种方法扩展到$ n $的较小值的理论，以$ n = 2、3 $和$ 4 $显示明确的结果。在离散的轻锥量化的背景下，我们根据Cayley-Hamilton定理制定了一个程序，用于确定在有限$ n $的情况下，大型$ n $理论的哪种状态变为无效。对于低洼的边界状态，我们发现平方群体除以$ g^2 n $，其中$ g $是量规耦合，对$ n $的依赖非常弱。 $ 1/n^2 $校正其大$ n $值的系数非常小。当伴随的费米无质量时，我们会观察到确切的脱生酸，从KAC-MOODY代数构建和电荷共轭对称性来解释。当将伴随费米昂的平方质量调整为$ g^2 n /π$时，我们发现频谱表现出玻色子 - 弗米恩脱整体的证据，与该模型的超对称性均以$ n $的任何值一致。
The mass spectrum of $1+1$-dimensional $\mathrm{SU}(N)$ gauge theory coupled to a Majorana fermion in the adjoint representation has been studied in the large $N$ limit using Light-Cone Quantization. Here we extend this approach to theories with small values of $N$, exhibiting explicit results for $N=2, 3$, and $4$. In the context of Discretized Light-Cone Quantization, we develop a procedure based on the Cayley-Hamilton theorem for determining which states of the large $N$ theory become null at finite $N$. For the low-lying bound states, we find that the squared masses divided by $g^2 N$, where $g$ is the gauge coupling, have very weak dependence on $N$. The coefficients of the $1/N^2$ corrections to their large $N$ values are surprisingly small. When the adjoint fermion is massless, we observe exact degeneracies that we explain in terms of a Kac-Moody algebra construction and charge conjugation symmetry. When the squared mass of the adjoint fermion is tuned to $g^2 N / π$, we find evidence that the spectrum exhibits boson-fermion degeneracies, in agreement with the supersymmetry of the model at any value of $N$.
