论文标题
旋转矩阵理论的全景
The Panorama of Spin Matrix Theory
论文作者
论文摘要
自旋矩阵理论描述了$ \ mathcal {n} = 4 $ sym理论的接近bps限制，这使我们能够探测有限的$ n $效应，例如d-branes和黑洞物理。在以前的作品中，我们开发了球形还原和自旋链方法，以构建各种限制的自旋矩阵理论。在本文中，通过考虑一个在信件方面是立方的增压$ \ Mathcal {q} $，我们构建了$ \ MATHCAL {N} = 4 $ SEMS的最大自旋矩阵理论的汉密尔顿，称为psu $ $（1,2 | 3） \ Mathcal {Q}^\ Dagger \} $。我们表明，在超对称性下，所产生的哈密顿量自动确定并明显不变。哈密顿量是由基本块制成的，这些区块变成了超级人。这种哈密顿量的新功能是将其分为d-terms和f-terms，它们在PSU $（1,2 | 3）$对称性和正定确定性下分别不变。由于可以通过关闭理论中的某些字母来获得所有其他自旋矩阵理论，因此可以获取$ \ mathcal {n} = 4 $ sym，我们认为我们的工作揭示了自旋矩阵理论的“全景”。
Spin Matrix theory describes near-BPS limits of $\mathcal{N}=4$ SYM theory, which enables us to probe finite $N$ effects like D-branes and black hole physics. In previous works, we have developed the spherical reduction and spin chain methods to construct Spin Matrix theory for various limits. In this paper, by considering a supercharge $\mathcal{Q}$ which is cubic in terms of the letters, we construct the Hamiltonian of the largest Spin Matrix theory of $\mathcal{N}=4$ SYM, called the PSU$(1,2|3)$ Spin Matrix theory, as $H = \{\mathcal{Q}, \mathcal{Q}^\dagger \}$. We show the resulting Hamiltonian is automatically positive definite and manifestly invariant under supersymmetry. The Hamiltonian is made of basic blocks which transform as supermultiplets. A novel feature of this Hamiltonian is its division into D-terms and F-terms that are separately invariant under PSU$(1,2|3)$ symmetry and positive definite. As all the other Spin Matrix theories arising from $\mathcal{N}=4$ SYM can be acquired by turning off certain letters in the theory, we consider our work as revealing the "Panorama" of Spin Matrix theory.
