AI 中文总结
研究\(\mathcal{N}=8\)超引力的四维紫外完备空间，通过4、5、6点EFT散射振幅树级因式分解及特殊宇称条件对4点威尔逊系数施加非线性约束，结合正性缩小允许区域，最终表明特定条件下仅留下维拉索罗 - 夏皮罗振幅。
AI 中文摘要
我们研究了\(\mathcal{N}=8\)超引力的四维紫外完备空间，其在低能下由具有最大超对称性和\(\mathrm{SU}(4)\times\mathrm{SU}(4)\)R-对称性的弱耦合有效场论（EFT）描述。我们表明，4、5和6点EFT散射振幅的树级因式分解，以及特定的“特殊宇称”条件，导致对4点威尔逊系数的非线性约束。这种特殊宇称是一种只能施加在标量振幅子集上的性质。将非线性约束与正性相结合，我们发现4点威尔逊系数的允许区域缩小到一个具有两个尖角的非凸域：一个是封闭超弦维拉索罗 - 夏皮罗振幅，另一个是在相同质量下交换每个自旋态的无限自旋塔振幅。我们通过数值和解析方法表明，在第一个质量水平附近要求有限数量的态仅留下维拉索罗 - 夏皮罗振幅。
英文摘要
We study the space of four-dimensional ultraviolet completions for $\mathcal{N}=8$ supergravity that are described at low energies by weakly-coupled effective field theories (EFTs) with maximal supersymmetry and $\mathrm{SU}(4)\times\mathrm{SU}(4)$ R-symmetry. We show that tree-level factorization of the 4-, 5-, and 6-point EFT scattering amplitudes, together with a certain ``peculiar parity'' condition, leads to nonlinear constraints on the 4-point Wilson coefficients. This peculiar parity is a property that can only be imposed on a subset of scalar amplitudes. Combining the nonlinear constraints with positivity, we find that the allowed region of 4-point Wilson coefficients is reduced to a non-convex domain with two sharp corners: one being the closed superstring Virasoro--Shapiro amplitude, the other an infinite spin tower amplitude exchanging states of every spin at the same mass. We show both numerically and analytically that requiring a finite number of states near the first mass level leaves only the Virasoro--Shapiro amplitude.
Comments35+9 pages, 2 figures, 3 tables
