论文标题
通过自举来解密最大的超然性原理
Deciphering the Maximal Transcendentality Principle via Bootstrap
论文作者
论文摘要
我们证明了一类形式的最大超朝外性原理，包括一般的两环最小构想，两环的三点外形要素为$ {\ rm tr}（f^2）$，以及$ {\ rm tr}（f^3）$的两环四点形式。我们的证明是基于最近开发的Bootstrap方法，该方法使用主体积分扩展的表示，以及在一般规格理论中通用的一些单位性削减。在两个平面$ \ mathcal $ \ mathcal {n} = 4 $ sym和纯YM理论中，首次获得了两环四元格形式的最大先验零件。该形式可以理解为希格斯 - 加luon振幅，涉及希格斯有效理论中的尺寸七个操作员。在这种情况下，我们发现$ \ MATHCAL {n} = 4 $ sym结果的最大先验部分与纯YM不同，并且差异是由于Gluino-loop贡献$ \ Mathcal {n} = 4 $ sym。相反，标量环的贡献没有最大的先验部分。因此，在正确识别基本夸克和伴随的Gluinos之后，最大的超然性原理仍具有$ \ MATHCAL {n} = 4 $ SYM和QCD的形式导致$ \ Mathcal {n} = 4 $ sym和QCD。这似乎是涉及费米恩环贡献的最大先验原则的第一个例子。作为另一个有趣的观察，我们发现半bps $ \ mathrm {tr}（ϕ^3）$ operator的四点形式是$ \ mathrm {tr}（f^3）$的构成块。
We prove the principle of maximal transcendentality for a class of form factors, including the general two-loop minimal form factors, the two-loop three-point form factor of ${\rm tr}(F^2)$, and the two-loop four-point form factor of ${\rm tr}(F^3)$. Our proof is based on a recently developed bootstrap method using the representation of master integral expansions, together with some unitarity cuts that are universal in general gauge theories. The maximally transcendental parts of the two-loop four-gluon form factor of $\mathrm{tr}(F^3)$ are obtained for the first time in both planar $\mathcal{N}=4$ SYM and pure YM theories. This form factor can be understood as the Higgs-plus-four-gluon amplitudes involving a dimension-seven operator in the Higgs effective theory. In this case, we find that the maximally transcendental part of the $\mathcal{N}=4$ SYM result is different from that of pure YM, and the discrepancy is due to the gluino-loop contributions in $\mathcal{N}=4$ SYM. In contrast, the scalar-loop contributions have no maximally transcendental parts. Thus, the maximal transcendentality principle still holds for the form factor results in $\mathcal{N}=4$ SYM and QCD, after a proper identification of the fundamental quarks and adjoint gluinos as $n_f \rightarrow 4N_c$. This seems to be the first example of the maximally transcendental principle that involves fermion-loop contributions. As another intriguing observation, we find that the four-point form factor of the half-BPS $\mathrm{tr}(ϕ^3)$ operator is precisely a building block in the form factor of $\mathrm{tr}(F^3)$.
