发表机构
National Taiwan University; National Center for Theoretical Sciences; Max Planck-IAS-NTU Center for Particle Physics, Cosmology and Geometry; University of Science and Technology of China（国立台湾大学; 国家理论科学中心; 马克斯·普朗克研究所-台湾大学粒子物理、宇宙学与几何中心; 中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过共线极限和标量奇偶性投影，证明了最大超对称理论中低能展开约束的所有阶次，并唯一确定了Veneziano振幅，同时指出选择Virasoro-Shapiro振幅需额外假设。
AI 中文摘要
近期研究表明，最大超对称性结合六点处特定的标量奇偶性条件，对四点有效场论振幅施加了非线性约束。包含幺正性的数值自举研究为最大超对称杨-米尔斯理论中的Veneziano振幅以及超引力中的Virasoro-Shapiro振幅（连同无限自旋替代方案）提供了证据。在本文中，我们建立了这些约束在低能展开中的所有阶次。推导使用了共线极限，其中三个三粒子因子化通道（或引力中的六个）同时在壳。标量奇偶性投影和单一离散R对称性消除了未知的六点余项，留下完全由四点因子化决定的三项主方程。求解这些方程证明了推测的指数形式，并提供了一个从正则前向极限重构完整振幅的映射。在明确的解析和正色散假设下，规范理论指数的固定反射偶部分决定了前向谱测度，并唯一地选择Veneziano振幅，有限自旋留数作为结果出现。在引力中，指数留下前向测度不确定：支持在单个质量层的测度重构出在该质量处具有无限多交换自旋的振幅。因此，最低质量极点处的有限自旋支持是选择Virasoro-Shapiro振幅所需的额外假设，在所述紫外框架内。
英文摘要
Recent work has shown that maximal supersymmetry, combined with a particular scalar-parity condition at six points, imposes nonlinear constraints on four-point effective field theory amplitudes. Numerical bootstrap studies incorporating unitarity provide evidence for the Veneziano amplitude in maximally supersymmetric Yang--Mills theory and for the Virasoro--Shapiro amplitude, together with infinite-spin alternatives, in supergravity. In this paper, we establish these constraints to all orders in the low-energy expansion. The derivation uses a collinear limit in which three three-particle factorization channels, or six in gravity, simultaneously go on shell. A scalar-parity projection and a single discrete R-symmetry eliminate the unknown six-point remainder, leaving three-term master equations determined entirely by four-point factorization. Solving these equations proves the conjectured exponential forms and provides a map that reconstructs the full amplitude from its regular forward limit. Under explicit analytic and positive dispersive assumptions, the fixed reflection-even part of the gauge-theory exponential determines the forward spectral measure and uniquely selects the Veneziano amplitude, with finite-spin residues emerging as a consequence. In gravity, the exponential leaves the forward measure undetermined: a measure supported at a single massive level reconstructs an amplitude with infinitely many exchanged spins at that mass. Finite-spin support at the lowest massive pole is therefore an additional assumption required to select the Virasoro--Shapiro amplitude within the stated ultraviolet framework.
Comments44 pages, 2 figures
