In this paper, we classify four-point local gluon S-matrices in arbitrary dimensions. This is along the same lines as [1] where four-point local photon S-matrices and graviton S-matrices were classified. We do the classification explicitly for gauge groups SO( N ) and SU( N ) for all N but our method is easily generalizable to other Lie groups. The construction involves combining not-necessarily-permutation-symmetric four-point S-matrices of photons and those of adjoint scalars into permutation symmetric four-point gluon S-matrix. We explicitly list both the components of the construction, i.e permutation symmetric as well as non-symmetric four point S-matrices, for both the photons as well as the adjoint scalars for arbitrary dimensions and for gauge groups SO( N ) and SU( N ) for all N . In this paper, we explicitly list the local Lagrangians that generate the local gluon S-matrices for D ≥ 9 and present the relevant counting for lower dimensions. Local Lagrangians for gluon S-matrices in lower dimensions can be written down following the same method. We also express the Yang-Mills four gluon S-matrix with gluon exchange in terms of our basis structures.

中文翻译：

---

四点局部胶子S矩阵的分类

在本文中，我们对任意维度的四点局部胶子 S 矩阵进行分类。这与对四点局部光子 S 矩阵和引力子 S 矩阵进行分类的 [1] 相同。我们明确地对所有 N 的规范群 SO( N ) 和 SU( N ) 进行分类，但我们的方法很容易推广到其他李群。该构造涉及将光子的不必要置换对称四点 S 矩阵和伴随标量的矩阵组合成置换对称四点胶子 S 矩阵。我们明确地列出了构造的两个组成部分，即置换对称和非对称四点 S 矩阵，对于任意维度的光子以及伴随标量和规范群 SO( N ) 和 SU( N ) 对于所有 N 。在本文中，我们明确列出了为 D ≥ 9 生成局部胶子 S 矩阵的局部拉格朗日函数，并提供了较低维度的相关计数。低维胶子 S 矩阵的局部拉格朗日可以按照相同的方法写出。我们还根据我们的基础结构表达了具有胶子交换的 Yang-Mills 四胶子 S 矩阵。