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arXiv 2403.08855hep-th
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弦与粒子散射振幅的普适分裂

A universal splitting of string and particle scattering amplitudes

Qu Cao, Jin Dong, Song He, Canxin Shi

AI总结:

提出了树级弦/粒子振幅的普适分裂行为,通过在 Mandelstam 变量子空间中分裂 Koba-Nielsen 因子,实现了多种理论振幅的因子化并扩展了软定理与平滑分裂。

摘要:

我们提出了标量、胶子和引力子的树级弦/粒子振幅的新分裂行为。我们在 Mandelstam 变量空间中识别出某些子空间,其中普适的 Koba-Nielsen 因子分裂为两部分(每部分带有离壳腿)。带有 Parke-Taylor 因子的开弦和闭弦振幅自然地因子化为两个弦 ${\it currents}$,这意味着 bi-adjoint $ϕ^3$ 振幅的分裂,并通过简单形变到统一的弦振幅,实现了非线性 sigma 模型和 Yang-Mills 标架理论中振幅的分裂;标量振幅的分裂对应于特殊的 Galileon。值得注意的是,当我们对涉及极化的 Lorentz 乘积施加类似约束时,玻色弦和超弦理论中的胶子和引力子振幅分裂为两个(弦)currents。该分裂的一个特殊情况蕴含了软定理,更一般地,它将近期提出的平滑分裂和零点附近的新因子化扩展到了所有这些理论。

英文摘要:

We propose a new splitting behavior of tree-level string/particle amplitudes for scalars, gluons and gravitons. We identify certain subspaces in the space of Mandelstam variables, where the universal Koba-Nielsen factor splits into two parts (each with an off-shell leg). Both open- and closed-string amplitudes with Parke-Taylor factors naturally factorize into two stringy ${\it currents}$, which implies the splitting of bi-adjoint $ϕ^3$ amplitudes and via a simple deformation to unified stringy amplitudes, the splitting of amplitudes in the non-linear sigma model and Yang-Mills-scalar theory; the same splitting holds for scalar amplitudes without color such as the special Galileon. Remarkably, if we impose similar constraints on Lorentz products involving polarizations, gluon and graviton amplitudes in bosonic string and superstring theories also split into two (stringy) currents. A special case of the splitting implies soft theorems, and more generally it extends recently proposed smooth splittings and new factorizations near zeros to all these theories.

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