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arXiv 1301.3028hep-thgr-qc
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D=6自对偶超引力的新陪集矩阵

New coset matrix for D=6 self-dual supergravity

Gérard Clément, Dmitri V. Gal'tsov

备注：
Section "Outlook" and refs. 10,23 edited. Relation to Sen's work is clarified in section 2. Journal version
发表信息：
JHEP 1303 (2013) 143
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摘要：

将最小六维超引力、最小五维超引力和四维爱因斯坦-麦克斯韦引力降维为三维，得到一个陪集序列$O(4,3)/(O(4)\times O(3))\supset G_{2(2)}/(SU(2)\times SU(2))\supset SU(2,1)/S(U(2)\times U(1))$，它们是彼此的不变子空间。然而，这些陪集的已知矩阵表示不适合实现这些嵌入，这可能是有用的解决方案生成。我们构造了一个新的表示的最大陪集的$7\times 7$实对称矩阵，并展示了如何选择不变子空间对应的低陪集的代数约束。新的矩阵表示也可以直接应用于最小五维超引力。由于全O（4，3）协方差，它比我们以前对陪集$G_{2(2)}/(SU(2)\times SU(2))$导出的简单.

英文摘要：

Toroidal reduction of minimal six-dimensional supergravity, minimal five-dimensional supergravity and four-dimensional Einstein-Maxwell gravity to three dimensions gives rise to a sequence of cosets $O(4,3)/(O(4)\times O(3))\supset G_{2(2)}/(SU(2)\times SU(2))\supset SU(2,1)/S(U(2)\times U(1))$ which are invariant subspaces of each other. The known matrix representations of these cosets, however, are not suitable to realize these embeddings which could be useful for solution generation. We construct a new representation of the largest coset in terms of $7\times 7$ real symmetric matrices and show how to select invariant subspaces corresponding to lower cosets by algebraic constraints. The new matrix representative may be also directly applied to minimal five-dimensional supergravity. Due to full O(4,3) covariance it is simpler than the one derived by us previously for the coset $G_{2(2)}/(SU(2)\times SU(2))$.

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