Scattering amplitudes and Wilson loops in twistor space
Scattering amplitudes and Wilson loops in twistor space
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DOI：
10.1088/1751-8113/44/45/454008
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发表时间：
2011-04
期刊：
影响因子：
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通讯作者：
T. Adamo;Mathew Bullimore;L. Mason;David Skinner
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文献类型：
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作者：
T. Adamo;Mathew Bullimore;L. Mason;David Skinner
本文回顾了超杨米尔斯威尔逊环、振幅及其对偶性的扭量方法的最新进展。威尔逊环和振幅是根据最大超对称杨-米尔斯理论的扭量作用从第一原理推导出来的。我们首先从扭量空间中轴向规范的扭量作用推导出规范理论振幅的 MHV 规则，并表明这产生了 Cachazo、Svrček 和 Witten 给出的原始动量空间版本。然后，我们继续使用（平面）MHV 规则从中获得动量扭量空间环被积函数的构造，并展示它如何作为扭量空间中全纯威尔逊环的期望值出现。我们解释了全纯威尔逊环和相关函数的某些光锥极限之间的联系。我们简要回顾了与扭量空间中的振幅相关的其他想法：扭量弦、扭量空间中的递归、用于引导奇点的格拉斯曼留数公式和作为多胞体的振幅。本文是《物理学杂志 A：数学与理论》特刊的特邀评论，专门讨论“规范理论中的散射振幅”。
This paper reviews the recent progress in twistor approaches to Wilson loops, amplitudes and their duality for super-Yang–Mills. Wilson loops and amplitudes are derived from first principles using the twistor action for maximally supersymmetric Yang–Mills theory. We start by deriving the MHV rules for gauge theory amplitudes from the twistor action in an axial gauge in twistor space, and show that this gives rise to the original momentum space version given by Cachazo, Svrček and Witten. We then go on to obtain from these the construction of the momentum twistor space loop integrand using (planar) MHV rules and show how it arises as the expectation value of a holomorphic Wilson loop in twistor space. We explain the connection between the holomorphic Wilson loop and certain light-cone limits of correlation functions. We give a brief review of other ideas in connection with amplitudes in twistor space: twistor-strings, recursion in twistor space, the Grassmannian residue formula for leading singularities and amplitudes as polytopes. This paper is an invited review for a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Scattering amplitudes in gauge theories’.