论文标题
六角形形式和边缘变形中的高级部门
Higher-rank sectors in the hexagon formalism and marginal deformations
论文作者
论文摘要
六边形方法为在$ \ MATHCAL {n} = 4 $ SUPER YANG-MILLS理论中以四个维度计算结构常数的计算提供了一个集成性框架。将三点函数切成两个六角形斑块，在该贴片上，频谱问题散布的远距离贝尔·安萨兹的激发在上面。为此，代表操作员的伯特州也需要切成两个部分。在等级的部门中，这种纠缠状态的构建非常简单，因此该方法的大多数应用都限于这种最简单的情况。在本文中，我们在$ psu（1,1 | 2）$部门中为运营商构建了纠缠状态，从嵌套的伯特·安萨兹（Bethe Ansatz）进口了最少的信息。对于具有多达三个高级运营商的相关器的样本相关器的样本集，对自由场理论进行了成功测试。此外，我们在理论的边际变形的情况下看一下相同的相关因子。虽然目前对六边形程序进行系统的修改仍然无法触及，但在实际应用中，未构造的幅度令人惊讶地有效，尤其是对于某个一定的一参数变形而言。
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.
