$N$：五维指数和AdS黑洞
The joy of factorization at large $N$: five-dimensional indices and AdS black holes
摘要：
我们讨论了具有全息对偶的五维超对称配分函数的大$N$分解性质。我们考虑流形上的配分函数的形式$\mathcal{M}= \mathcal{M}_3 \times S^2_ε$，其中$ε$是一个旋转的等变参数。我们表明，当$\mathcal{M}_3$是一个压扁的三球，大$N$配分函数可以通过胶合与简单的物理量相关的基本块。对于$\mathcal{M}_3=Σ_\mathfrak{g} \times S^1$理论的各种可观测量也是如此，其中$Σ_\mathfrak{g}$是亏格$\mathfrak{g}$的黎曼曲面，并且对于配分函数也是如此，配分函数对应于拓扑扭曲指数或混合指数。这概括了三维和四维的结果，并正确地再现了已知的黑色物体在AdS $_6 \times_{w} S^4$和AdS $_7\times S^4$的熵。我们还提供了超对称的背景，并明确执行本地化的混合指数$Σ_\mathfrak{g} \times S^1 \times S^2_ε$，填补了文献中的空白。
英文摘要：
We discuss the large $N$ factorization properties of five-dimensional supersymmetric partition functions for CFT with a holographic dual. We consider partition functions on manifolds of the form $\mathcal{M}= \mathcal{M}_3 \times S^2_ε$, where $ε$ is an equivariant parameter for rotation. We show that, when $\mathcal{M}_3$ is a squashed three-sphere, the large $N$ partition functions can be obtained by gluing elementary blocks associated with simple physical quantities. The same is true for various observables of the theories on $\mathcal{M}_3=Σ_\mathfrak{g} \times S^1$, where $Σ_\mathfrak{g}$ is a Riemann surface of genus $\mathfrak{g}$, and, with a natural assumption on the form of the saddle point, also for the partition function, corresponding to either the topologically twisted index or a mixed one. This generalizes results in three and four dimensions and correctly reproduces the entropy of known black objects in AdS$_6 \times_{w} S^4$ and AdS$_7\times S^4$. We also provide the supersymmetric background and explicitly perform localization for the mixed index on $Σ_\mathfrak{g} \times S^1 \times S^2_ε$, filling a gap in the literature.
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