Subleading-color contributions to gluon-gluon scattering in = 4 SYM theory and relations to = 8 supergravity
Subleading-color contributions to gluon-gluon scattering in = 4 SYM theory and relations to = 8 supergravity
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= 4 SYM 理论中副主色对胶子-胶子散射的贡献以及与 = 8 超重力的关系
DOI：
10.1088/1126-6708/2008/11/018
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发表时间：
2008
影响因子：
5.4
通讯作者：
H. Schnitzer
中科院分区：
文献类型：
--
作者：
S. Naculich;H. Nastase;H. Schnitzer
在=4超对称SU(N)Yang-Mills理论中，我们研究了亚显色(非平面)对四胶子散射振幅的贡献。利用Catani、Sterman和Tejeda-Yeomans的形式，我们给出了三圈以下所有副导色L圈振幅的红外发散贡献的显式表达式，并对任意L的红外行为作出了一些猜想。我们还导出了几个有趣的副导色单圈和两圈四圈四胶子振幅与=8超引力的四重力子振幅之间的关系。确切的单圈和双圈=8超重力振幅可以分别用单圈和双圈N无关=4SYM振幅来表示，但对更高圈的自然概括失败了，尽管有一个关于‘t Hooft图的简单解释。我们还发现，至少通过两个回路，=4SYM理论的次前色振幅具有一致的超越性(前色振幅也是如此)。此外，用低环幅度表示环幅的IR发散贡献的=4 SYM Catani算子也被证明具有一致的超越性，是QCD Catani算子的最大超越性部分。
We study the subleading-color (nonplanar) contributions to the four-gluon scattering amplitudes in = 4 supersymmetric SU(N) Yang-Mills theory. Using the formalisms of Catani and of Sterman and Tejeda-Yeomans, we develop explicit expressions for the infrared-divergent contributions of all the subleading-color L-loop amplitudes up to three loops, and make some conjectures for the IR behavior for arbitrary L. We also derive several intriguing relations between the subleading-color one- and two-loop four-gluon amplitudes and the four-graviton amplitudes of = 8 supergravity. The exact one- and two-loop = 8 supergravity amplitudes can be expressed in terms of the one- and two-loop N-independent = 4 SYM amplitudes respectively, but the natural generalization to higher loops fails, despite having a simple interpretation in terms of the 't Hooft picture. We also find that, at least through two loops, the subleading-color amplitudes of = 4 SYM theory have uniform transcendentality (as do the leading-color amplitudes). Moreover, the = 4 SYM Catani operators, which express the IR-divergent contributions of loop amplitudes in terms of lower-loop amplitudes, are also shown to have uniform transcendentality, and to be the maximum transcendentality piece of the QCD Catani operators.