On G/H geometry and its use in M-theory compactifications
On G/H geometry and its use in M-theory compactifications
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关于 G/H 几何及其在 M 理论紧化中的应用
DOI：
10.1006/aphy.2000.6097
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发表时间：
1999
影响因子：
3
通讯作者：
L. Castellani
中科院分区：
文献类型：
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作者：
L. Castellani
摘要回顾了陪集空间的黎曼几何，重点讨论了它在超重力和M理论紧化中的应用。将重标度陪集流形的联络和曲率公式推广到非对角线Killing度量的情形。并以N010空间为例进行了详细的讨论。这是陪集流形Npqr=G/H=SU(3)×U(1)/U(1)×U(1)的一个子类，是刻画H嵌入G的整数p，q，Ur。我们研究了N010的实现为G/H=SU(3)×SU(2)/U(1)×SU(2)(具有SU(2)∈H对角嵌入到G中)。对于一个特殊的G对称重标度，存在三个杀戮旋量，这意味着在D=11超重力的AdS4×N010压缩中N=3超对称性。这个重新标度的N010空间对AdS4/CFT3对应特别有意义，它的SU(3)×SU(2)等距实现对于Kaluza-Klein模的OSP(4|3)分类是必不可少的。
Abstract The Riemannian geometry of coset spaces is reviewed, with emphasis on its applications to supergravity and M-theory compactifications. Formulae for the connection and curvature of rescaled coset manifolds are generalized to the case of nondiagonal Killing metrics. The example of the N010 spaces is discussed in detail. These are a subclass of the coset manifolds Npqr=G/H=SU(3)×U(1)/U(1)×U(1), the integers p, q, r characterizing the embedding of H in G. We study the realization of N010 as G/H=SU(3)×SU(2)/U(1)×SU(2) (with diagonal embedding of the SU(2)∈H into G). For a particular G-symmetric rescaling there exist three Killing spinors, implying N=3 supersymmetry in the AdS4×N010 compactification of D=11 supergravity. This rescaled N010 space is of particular interest for the AdS4/CFT3 correspondence, and its SU(3)×SU(2) isometric realization is essential for the OSp(4 ∣ 3) classification of the Kaluza–Klein modes.