发表机构
School of Mathematics and Hamilton Mathematics Institute, Trinity College, Dublin 2, Ireland; Okinawa Institute of Science and Technology (OIST), Onna, Okinawa, Japan（都柏林三一学院数学与汉密尔顿数学研究所; 冲绳科学技术大学院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用维度正则化下任意重数和螺旋度的平面N=4 SYM单圈振幅，通过朗道分析与簇邻接揭示其结构，证明符号满足簇邻接并推测更强的簇性质。
AI 中文摘要
广义幺正性、朗道分析与簇邻接编码了散射振幅的互补方面。我们使用维度正则化下任意重数和任意螺旋度的平面 $\mathcal N=4$ SYM 单圈振幅，使其界面明确化。权重二符号分解为一个LS部分（其中最大割主导奇异性提供系数，与嵌套割相关的朗道轨迹组织有序符号条目）、一个代数四质量扇区以及剩余项。由单个箱式积分贡献的某些字母的相消以及进一步的简化，可通过箱式系数间的双质量三角形关系来解释。我们利用类似BCFW的全局留数定理应用证明了这些关系，并表明它们可以几何上理解为通过投影三重割的圈几何获得的树级amplituhedron中同一区域的不同剖分。然后我们证明，完整的理性符号（包括其红外发散部分）在旗簇代数 $\mathrm{Fl}_{2,4;n}$ 中满足所有重数和螺旋度的簇邻接。在仅依赖于动量扭量四括号的扇区内，我们推测所有螺旋度在 $\operatorname{Gr}(4,n)$ 中具有更强的簇性质，并证明NMHV振幅的情况：振幅允许一个表示，其中每个系数的每个极点与两个符号条目兼容。最后，我们观察到代数四质量字母虽非理性，却展现出一种暗示性的Sklyanin括号模式。
英文摘要
Generalized unitarity, Landau analysis, and cluster adjacency encode complementary aspects of scattering amplitudes. We use one-loop planar $\mathcal N=4$ SYM amplitudes in dimensional regularization, at arbitrary multiplicity and helicity, to make their interface explicit. The weight-two symbol decomposes into an LS part, in which maximal-cut leading singularities furnish the coefficients and Landau loci associated with nested cuts organize the ordered symbol entries, an algebraic four-mass sector, and residual terms. Cancellations of certain letters contributed by individual box integrals, as well as further simplifications, are explained by the two-mass triangle relations among box coefficients. We prove these relations using a BCFW-like application of the global residue theorem and show that they can be understood geometrically as different dissections of the same region in the tree amplituhedron obtained by projecting the loop geometry of a triple cut. We then prove that the full rational symbol, including its infrared-divergent part, obeys cluster adjacency in the flag cluster algebra $\mathrm{Fl}_{2,4;n}$ for all multiplicities and helicities. Within the sector depending only on momentum-twistor four-brackets, we conjecture a stronger cluster property in $\operatorname{Gr}(4,n)$ for all helicities and prove it for NMHV amplitudes: the amplitude admits a representation in which every pole of each coefficient is compatible with both symbol entries. Finally, we observe that the algebraic four-mass letters, although non-rational, exhibit a suggestive Sklyanin-bracket pattern.
Comments55 pages, 7 figures
