Quantum gravity in ${\mathrm{AdS}}_7\times {\mathrm{S}}^4$ is dual to a six-dimensional (6D) superconformal field theory, known as the 6D (2,0) theory, which is very challenging to describe because it lacks a conventional Lagrangian description. On the other hand, certain null reductions of the 6D (2,0) theory give rise to 5D Lagrangian theories with SU(1,3) spacetime symmetry, SO(5) R symmetry, and 24 supercharges. This appears to be closely related to the superconformal group of a 3D superconformal Chern-Simons theory known as the Aharony-Bergman-Jafferis-Maldacena theory, which is believed to be integrable in the planar limit, if one exchanges the role of conformal and R symmetry. In this Letter, we construct a representation of the 5D superconformal group using 6D supertwistors and show that it admits an infinite dimensional extension known as Yangian symmetry, which opens up the possibility that these 5D theories are exactly solvable in the planar limit.

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杨安五维对称

量子引力${\mathrm{AdS}}_7\times {\mathrm{小号}}^{\mathrm{4个}}$是六维 (6D) 超共形场论的对偶，称为 6D (2,0) 理论，描述起来非常具有挑战性，因为它缺乏传统的拉格朗日描述。另一方面，6D (2,0) 理论的某些零位缩减产生具有 SU(1,3) 时空对称性、SO(5) R 对称性和 24 个增压的 5D 拉格朗日理论。这似乎与被称为 Aharony-Bergman-Jafferis-Maldacena 理论的 3D 超共形 Chern-Simons 理论的超共形群密切相关，如果交换共形和 R 的作用，该理论被认为在平面极限中是可积的对称。在这封信中，我们使用 6D 超扭曲构造了 5D 超共形群的表示，并表明它允许无限维扩展，称为 Yangian 对称性，