积分 ABJM 理论中的完整四圈负几何与所有圈梯型负几何
Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory
AI总结：
本文利用 Mellin 变换积分 ABJM 理论的四圈及所有圈梯型负几何，提取尖峰反常维度贡献，并揭示四圈仅树型几何有效、梯型几何不产生 ζ_3 与 ζ_5 等结构。
摘要：
将四点 ABJM amplituhedron 分解为负几何，可产生振幅对数的紧凑被积函数，使红外发散仅来自最后一次圈积分，由此可计算 ABJM 理论的尖峰反常维度。在本简报中，我们通过一种基于 Mellin 变换的方法，对所有四圈负几何以及一类特殊的所有圈梯型负几何，积分其 L 圈负几何中的 L−1 个圈动量，并从这些有限量中提取对尖峰反常维度的相应贡献。我们发现，在 L=4 时，盒型负几何的红外发散弱于其他负几何，因此在 L=4 时只有树型负几何对尖峰反常维度有贡献。对于所有圈梯型负几何，我们证明并猜想了 Mellin 空间中作为积分方程的若干递归结构，并发现它们不能像 ζ_3、ζ_5 那样向尖峰反常维度贡献 zeta 值。
英文摘要：
The decomposition of the four-point ABJM amplituhedron into negative geometries produces compact integrands of logarithmic of amplitudes such that the infrared divergence only comes from the last loop integration, from which we can compute the cusp anomalous dimension of the ABJM theory. In this note, we integrate $L-1$ loop momenta of the $L$-loop negative geometries for all four-loop negative geometries and a special class of all-loop ladder-type negative geometries by a method based on Mellin transformation, and from these finite quantities we extract the corresponding contribution to the cusp anomalous dimension. We find that the infrared divergence of a box-type negative geometry at $L=4$ is weaker than other negative geometries, then only tree-type negative geometries contribute to the cusp anomalous dimension at $L=4$. For the all-loop ladder-type negative geometries, we prove and conjecture some recursive structures as integral equations in Mellin space and find that they cannot contribute zeta values like $ζ_3,ζ_5$ to the cusp anomalous dimension.
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