论文标题
超级阳米尔斯理论中的一环非平面异常维度
One-Loop Non-Planar Anomalous Dimensions in Super Yang-Mills Theory
论文作者
论文摘要
我们考虑最大超对称的阳米尔理论中的非平面单环异常尺寸及其略有变形的类似物。使用伯特状态的基础，我们计算扩张算子的基质元素，并根据外壳标量产品和类似六边形的功能找到紧凑的表达式。然后，我们使用非分类量子力学扰动理论来计算运算符尺寸的领先$ 1/n^2 $校正，并以$ r $ charge中的subleading订单计算两种激励状态的大$ r $ charge限制。最后，我们从数值上研究了这些理论的水平间距的分布，并表明它们从无限$ n $的集成系统的泊松分布过渡到有限$ n $的量子混乱系统的Goe Wigner-Dyson分布。
We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use non-degenerate quantum-mechanical perturbation theory to compute the leading $1/N^2$ corrections to operator dimensions and as an example compute the large $R$-charge limit for two-excitation states through subleading order in the $R$-charge. Finally, we numerically study the distribution of level spacings for these theories and show that they transition from the Poisson distribution for integrable systems at infinite $N$ to the GOE Wigner-Dyson distribution for quantum chaotic systems at finite $N$.
