发表机构
Yale University; National Taiwan University; National Center for Theoretical Sciences; Max Planck-IAS-NTU Center for Particle Physics, Cosmology and Geometry; Brown University（耶鲁大学; 台湾大学; 国家理论科学中心; 马克斯·普朗克IAS-台大粒子物理、宇宙学与几何中心; 布朗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究分析四维N=4杨-米尔斯耦合N=4超引力的树级完备性，结合因式分解、超对称等条件得到杂合弦与无穷自旋塔振幅的结构，通过数值与解析分析限定了耦合比等参数。
AI 中文摘要
我们研究四维$\boldsymbol{\textit{N}=4}$杨-米尔斯理论耦合$\boldsymbol{\textit{N}=4}$超引力的树级完备性。六点因式分解与超对称沃德恒等式，结合对标量接触项的宇称奇异性限制，对四胶子振幅的单迹和双迹威尔逊系数$a_{k,q}$与$b_{k,q}$施加了非线性关系。最简单的关系$\boldsymbol{\textit{\u03BA}^2a_{0,0}=0}$排除了非零引力耦合下的单迹$F^4$相互作用，尽管其与四点超对称兼容。在该引力分支上，五个双迹参数通过$a_{7,q}$和$b_{8,q}$确定所有系数，这些系数可由通用指数生成形式重现。杂合弦理论与一族无穷自旋塔（IST）振幅均实现该结构。将这些关系与$SO(N)$色道中的色散关系和分波正性结合，得到一条狭窄的数值带，其边界由杂合弦与最简单IST振幅严格限定。自旋依赖的质量间隙排除了IST谱，进一步将区域定位于杂合弦轨迹附近。对最简单IST的解析幺正性分析给出$\boldsymbol{\textit{N}\u226448}$和$\boldsymbol{\textit{g}^2/(\boldsymbol{\textit{\u03BA}^2\boldsymbol{\textit{m}}^2})\u22644}$，与杂合弦振幅的上限匹配，其中$m$为第一质量级的质量。沿杂合弦轨迹，数值界还在$\boldsymbol{\textit{N}=48}$处严格约束了规范-引力耦合比。
英文摘要
We study tree-level completions of four-dimensional $\mathcal N=4$ Yang--Mills theory coupled to $\mathcal N=4$ supergravity. Six-point factorization and supersymmetry Ward identities, supplemented by a peculiar-parity restriction on scalar contact terms, impose nonlinear relations between the single- and double-trace Wilson coefficients, $a_{k,q}$ and $b_{k,q}$, of the four-gluon amplitude. The simplest relation, $κ^2a_{0,0}=0$, excludes the single-trace $F^4$ interaction at nonzero gravitational coupling, despite its compatibility with four-point supersymmetry. On this gravitational branch, five double-trace parameters determine all coefficients through $a_{7,q}$ and $b_{8,q}$, which are reproduced by a common exponential generating form. Both the heterotic string and a family of infinite-spin-tower (IST) amplitudes realize this structure. Combining these relations with dispersion relations and partial-wave positivity in $SO(N)$ color channels yields a narrow numerical band closely bounded by the heterotic and simplest IST amplitudes. A spin-dependent mass gap excludes the IST spectrum and further localizes the region near the heterotic trajectory. An analytic unitarity analysis of the simplest IST gives $N\leq48$ and $g^2/(κ^2 m^2)\leq4$, matching the upper limits of the heterotic amplitude, where $m$ is the mass of the first massive level. Along the heterotic trajectory, the numerical bounds also sharply constrain the gauge-to-gravity coupling ratio at $N=48$.
Comments32 pages, 6 figures
