Einstein manifolds and conformal field theories
Einstein manifolds and conformal field theories
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爱因斯坦流形和共形场论
DOI：
10.1103/physrevd.59.025006
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发表时间：
1998
影响因子：
5
通讯作者：
S. Gubser
中科院分区：
文献类型：
--
作者：
S. Gubser
鉴于反\char21{}德西特空间共形场论对应关系，很自然地尝试通过对爱因斯坦流形和反\char21{}德西特空间的乘积进行超重力紧致化，在大N、强耦合极限下定义共形场论。我们考虑五维流形 ${T}^{\mathrm{pq}}$，它们是陪集空间 $[\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)]/\mathrm{U}(1)。$ 中心电荷和手征谱的一部分分别根据${T}^{\mathrm{pq}}$ 和标量拉普拉斯的频谱。在所考虑的流形中，只有 ${T}^{11}$ 承认任何超对称性：正是这个流形表征了与圆锥形奇点处的大量 $D3$-膜相对应的超重力解，这是 Klebanov 和 Witten 最近讨论的。通过反常三点函数的场论分析，我们能够重现超引力为 ${T}^{11}$ 理论预测的中心电荷：它是 $\mathcal{N}=2{\mathbf{Z}}_{2}$ 轨道理论的中心电荷 $\frac{27}{32}$，它通过重正化群流下降。
In light of the anti\char21{}de Sitter space conformal field theory correspondence, it is natural to try to define a conformal field theory in a large N, strong coupling limit via a supergravity compactification on the product of an Einstein manifold and anti\char21{}de Sitter space. We consider the five-dimensional manifolds ${T}^{\mathrm{pq}}$ which are coset spaces $[\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)]/\mathrm{U}(1).$ The central charge and a part of the chiral spectrum are calculated, respectively, from the volume of ${T}^{\mathrm{pq}}$ and the spectrum of the scalar Laplacian. Of the manifolds considered, only ${T}^{11}$ admits any supersymmetry: it is this manifold which characterizes the supergravity solution corresponding to a large number of $D3$-branes at a conifold singularity, discussed recently by Klebanov and Witten. Through a field theory analysis of anomalous three point functions we are able to reproduce the central charge predicted for the ${T}^{11}$ theory by supergravity: it is $\frac{27}{32}$ of the central charge of the $\mathcal{N}=2{\mathbf{Z}}_{2}$ orbifold theory from which it descends via a renormalization group flow.