We compute the non-planar contribution to the universal anomalous dimension of twist-two operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at four loops through Lorentz spin eighteen. Exploiting the results of this and our previous calculations along with recent analytic results for the cusp anomalous dimension and some expected analytic properties, we reconstruct a general expression valid for arbitrary Lorentz spin. We study various properties of this general result, such as its large-spin limit, its small-x limit, and others. In particular, we present a prediction for the non-planar contribution to the anomalous dimension of the single-magnon operator in the β-deformed version of the theory.

我们计算了两个平面算子中第二个算子的普遍异常维的非平面贡献 $\mathcal{ñ}=4$超对称的杨米尔斯理论在通过洛伦兹自旋的四个循环中旋转了18个。利用该结果和我们先前的计算结果，以及针对尖端异常尺寸和某些预期分析性质的最新分析结果，我们重建了对任意Lorentz自旋有效的通用表达式。我们研究了此一般结果的各种属性，例如，大旋转极限，小x极限等。特别是，我们提出了在理论的β变形版本中非平面对单磁子算子异常维度贡献的预测。