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arXiv 0806.0685hep-th
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Young Diagrams中的几何

Geometries from Young Diagrams

Robert de Mello Koch

备注：
31 pages; v2: presentation improved
发表信息：
JHEP 0811:061,2008
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摘要：

IIB型弦理论在渐近AdS $_5\times$ S $^5$的时空上可以用四维${\cal N}=4$超级杨-米尔斯理论来定义。弦论的六个维度在杨-米尔斯理论中被全息重建。在这篇文章中，我们将研究这些维度和这些维度中的局部物理是如何出现的。我们重新组织的${1\over 2}$ BPS部门的场论的舒尔多项式重写它的动力学。这些多项式的杨图标记可以被看作是一个簿记设备，它总结了如何构造的运营商。我们表明，额外的全息维度的几何方面被捕获非常自然的杨图。位于体块中特定位置的引力子对应于在杨氏图上特定位置添加的盒子。

英文摘要：

Type IIB string theory on spacetimes that are asymptotically AdS$_5\times$S$^5$ can be defined using four dimensional ${\cal N}=4$ super Yang-Mills theory. Six of the dimensions of the string theory are holographically reconstructed in the Yang-Mills theory. In this article we study how these dimensions and local physics in these dimensions emerge. We reorganize the dynamics of the ${1\over 2}$ BPS sector of the field theory by rewriting it in terms of Schur polynomials. The Young diagram labeling of these polynomials can be viewed as a book keeping device which summarizes how the operator is constructed. We show that aspects of the geometry of the extra holographic dimensions are captured very naturally by the Young diagram. Gravitons which are localized at a specific position in the bulk correspond to boxes added at a specific location on the Young diagram.

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