六边形形式中的高阶扇区和边缘变形
Higher-rank sectors in the hexagon formalism and marginal deformations
摘要：
六边形方法提供了一个计算四维空间$\mathcal{N}=4$超杨-米尔斯理论结构常数的可积性框架。将三点函数切割成两个六边形曲面片，使谱问题中的长程Bethe模的激发散射在这两个六边形曲面片上。为此，代表运算符的Bethe状态也需要被切成两部分。在一阶扇区中，这种纠缠态的构造相当简单，因此该方法的大多数应用迄今仅限于这种最简单的情况。在这篇文章中，我们构造的$psu(1,1|2)$部门的运营商的纠缠态，从嵌套的Bethe的纠缠引入最少的信息。这一想法是成功地测试对自由场论的样本集，最多三个更高的排名运营商的竞争对手。此外，我们看看在理论的边缘变形的存在下，相同的放大器。虽然六边形程序的系统修改目前仍然遥不可及，但在实际应用中，未变形的振幅是令人惊讶的有效的，特别是对于某些单参数变形。
英文摘要：
The hexagon approach provides an integrability framework for the computation of structure constants in $\mathcal{N}=4$ super Yang--Mills theory in four dimensions. Three-point functions are cut into two hexagonal patches, on which the excitations of the long-range Bethe ansatz of the spectrum problem scatter. To this end, the Bethe states representing the operators also need to be cut into two parts. In rank-one sectors such entangled states are fairly straightforward to construct so that most applications of the method have so far been restricted to this simplest case. In this article we construct entangled states for operators in $psu(1,1|2)$ sectors, importing a minimum of information from the nested Bethe ansatz. The idea is successfully tested against free field theory for a sample set of correlators with up to three higher-rank operators. Further, we take a look at the same correlators in the presence of marginal deformations of the theory. While a systematic modification of the hexagon procedure remains out of reach for now, in practical applications the undeformed amplitudes are surprisingly efficient, especially for a certain one-parameter deformation.
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