发表机构
Science and Technology Directorate, U.S. Department of Homeland Security（美国国土安全部科技总局）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在平面四维极大超对称规范理论中，证明已知四点振幅的六点约束可实现任意多重度下的振幅完备化，通过特定构造方法确定系数并满足对称性与因子化条件。
AI 中文摘要
我们证明，在平面四维极大超对称规范理论中，已知的关于四点振幅的六点约束足以实现任意多重度下的完备化。我们将无质量树振幅构造为导数展开中的形式级数，该级数以标准超对称杨-米尔斯三点振幅、未破缺的R-对称性以及仅含外部标量的振幅的宇称不变性为基础，且保持标量标签固定。对于正的领头四点接触系数，对数参数化中的偶系数是固定的，而所有奇系数的实序列可通过所有导数阶的完备化来实现。该构造利用了场论Kawai-Lewellen-Tye双线性形式及球积分的归一化矩阵，对其矩阵对数的齐次分量取指数可独立改变奇系数，同时保持定域性和通过完整无质量多重态的因子化。因此，六点条件是此类完备化的必要且充分条件，一旦更高点接触相互作用与相同对称性及因子化条件一致地选取，更高多重度的一致性不会对这些四点系数施加进一步限制。
英文摘要
We show that the known six-point constraints on four-point amplitudes are sufficient for completion at arbitrary multiplicity in planar, four-dimensional maximally supersymmetric gauge theory. We construct massless tree amplitudes as formal series in the derivative expansion, with the standard supersymmetric Yang-Mills three-point amplitudes, unbroken R-symmetry, and parity invariance of amplitudes with only external scalars, holding the scalar labels fixed. For a positive leading four-point contact coefficient, the even coefficients in the logarithmic parameterization are fixed, while every real sequence of odd coefficients is realized by a completion at all derivative orders. The construction uses the field-theory Kawai-Lewellen-Tye bilinear and normalized matrices of sphere integrals. Exponentiating homogeneous components of their matrix logarithms varies the odd coefficients independently while preserving locality and factorization through the complete massless multiplet. The six-point conditions are therefore necessary and sufficient for such a completion. Higher-multiplicity consistency imposes no further restrictions on these four-point coefficients once the higher-point contact interactions are chosen consistently with the same symmetries and factorization conditions.
Comments27 pages
