Veneziano振幅的六点一致性与唯一性
Six-point consistency and uniqueness of the Veneziano amplitude
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中文总结 AI 辅助
本文通过结合六点一致性与低阶超对称关系，在亚纯类中证明Veneziano四点振幅的唯一性，并确定其全部极点与留数。
中文摘要 AI 辅助
我们通过将六点一致性与一个已知的低阶超对称关系相结合，在亚纯函数类中确立了Veneziano四点振幅的唯一性。我们考虑四维平面树级散射，涉及无质量极大超对称矢量多重态，并附加标量宇称条件。超对称Ward恒等式之差将无质量因子化留数分离出来，并消除了在共同运动学极限下所有允许的规则贡献。所得函数方程在每一导数阶均成立，并在固定Yang-Mills耦合下，扣除无质量极点后，从前向函数确定所有角依赖。对于具有简单平面极点、与零质量间隔的正质量平方极点非空谱、标量留数分波展开中非负系数以及精确的无减除前向色散关系的联合亚纯振幅，仅极点位置保持自由。正性约束了它们的间隔。低阶关系饱和了一个尖锐的谱不等式，要求无限序列等间距的质量平方极点。因此，耦合和第一个大质量极点位置确定了完整的四点函数及所有留数，无需初始有限自旋限制。
英文摘要
We establish uniqueness of the Veneziano four-point amplitude in a meromorphic class by combining six-point consistency with a known low-order supersymmetry relation. We consider planar tree-level scattering in four dimensions with a massless maximally supersymmetric vector multiplet and an additional scalar parity condition. A difference of supersymmetry Ward identities isolates massless factorization residues and eliminates every permitted contribution regular in a common kinematic limit. The resulting functional equation holds at every derivative order and fixes all angular dependence from the forward function after subtraction of the massless poles, at fixed Yang-Mills coupling. For a jointly meromorphic amplitude with simple planar poles, a nonempty spectrum of positive mass-squared poles separated from zero by a mass gap, nonnegative coefficients in the partial-wave expansions of scalar residues, and an exact unsubtracted forward dispersion relation, only the pole positions remain free. Positivity bounds their separation. The low-order relation saturates a sharp spectral inequality, requiring an infinite sequence of equally spaced mass-squared poles. The coupling and first massive pole position therefore determine the complete four-point function and all residues, without an initial finite-spin restriction.
