论文标题
IKKT-MATRIX模型的扭曲描述
A Twistorial Description of the IKKT-Matrix Model
论文作者
论文摘要
我们将模糊4-Sphere $ S_N^4 $视为IKKT矩阵模型的背景，并在半经典限制中探索$ S_N^4 $和模糊扭曲器空间之间的关系。给出了IKKT-MATRIX模型的新颖描述，该模型给出了旋转指数，这让人联想到$ \ Mathcal {n} = 4 $ $ 4D $中的超级超对方Yang-Mills（Sym）。在模糊的扭曲空间上，IKKT模型的相互作用是重力类型。 IKKT模型以HS-IKKT为hs-ikkt在模糊扭曲器空间上出现的高自旋（HS）仪表理论被证明是$ \ Mathcal {n} = 4 $ syms的更高旋转扩展，其顶点具有两个以上的衍生物。我们使用Penrose变换获得了（欧几里得）的时空作用。尽管这是一种引力理论，但它具有许多功能，其中Yang-Mills的较高自旋扩展在Arxiv中获得的$ 4D $平面空间：2105.12782，ARXIV：2107.04500。 HS-IKKT的树级幅度以半古典扁平极限进行了研究。 IKKT模型的自与双向扇区是通过丢弃立方和四分之一相互作用的某些部分来获得的，这证明可以减少对交换变形的投影式扭曲器空间的BF型动作。
We consider the fuzzy 4-sphere $S_N^4$ as a background in the IKKT matrix model and explore the relation between $S_N^4$ and fuzzy twistor space in the semi-classical limit. A novel description for the IKKT-matrix model in terms of spinorial indices is given, which is reminiscent of $\mathcal{N}=4$ super-symmetric Yang-Mills (SYM) in $4d$. On fuzzy twistor space, the interactions of the IKKT model are of gravitational type. The higher-spin (HS) gauge theory emerging in this limit from the IKKT model, denoted as HS-IKKT, on fuzzy twistor space is shown to be a higher-spin extension of $\mathcal{N}=4$ SYM, with vertices that have more than two derivatives. We obtain its (Euclidean) spacetime action using the Penrose transform. Although this is a gravitational theory, it shares many features with the higher-spin extensions of Yang-Mills in $4d$ flat space obtained in arXiv:2105.12782, arXiv:2107.04500. The tree-level amplitudes of the HS-IKKT are studied in the semi-classical flat limit. The self-dual sector of the IKKT model is obtained by dropping some parts of the cubic- and the quartic interactions, which is shown to reduce to a BF-type action on commutative deformed projective twistor space.
