Higher dimensional geometries related to fuzzy odd-dimensional spheres
Higher dimensional geometries related to fuzzy odd-dimensional spheres
复制标题
与模糊奇维球体相关的高维几何
DOI：
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发表时间：
2002
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通讯作者：
S. Ramgoolam
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作者：
S. Ramgoolam
在引文{Guram}之后，我们研究了偶数m作为候选模糊奇球时？i=1mxi2=1的SO(M)协变矩阵实现。对于模糊四球面，这些矩阵代数比球面本身包含更多的自由度，并且变量的全集具有高维陪集的几何描述。模糊S2k？1与高维陪集SO(2k)/U(1)？U(k？1)。这些陪集是丛，其中基和纤维是厄米特对称空间。与模糊三球面有关的矩阵代数的生成元和关系的详细形式表明，模糊三球面的矩阵作用是允许模糊球面作为解的。将这些矩阵作用与BFSS、IKKT、BMN等矩阵模型进行了比较。模糊奇球的几何和组合学引出了关于矩阵理论的横向五膜问题和5膜的熵随膜数的奇异标度的一些注记。
We study SO(m) covariant matrix realizations of ?i = 1mXi2 = 1 for even m as candidate fuzzy odd spheres following cite{guram}. As for the fuzzy four sphere, these matrix algebras contain more degrees of freedom than the sphere itself and the full set of variables has a geometrical description in terms of a higher dimensional coset. The fuzzy S2k?1 is related to a higher dimensional coset SO(2k)/U(1) ? U(k?1). These cosets are bundles where base and fibre are hermitean symmetric spaces. The detailed form of the generators and relations for the matrix algebras related to the fuzzy three-spheres suggests matrix actions which admit the fuzzy spheres as solutions. These matrix actions are compared with the BFSS, IKKT and BMN matrix models as well as some others. The geometry and combinatorics of fuzzy odd spheres lead to some remarks on the transverse five-brane problem of matrix theories and the exotic scaling of the entropy of 5-branes with the brane number.