论文标题
$ n $和黑洞的5D超符号指数
The 5d Superconformal Index at Large $N$ and Black Holes
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
We study the large $N$ limit of the superconformal index of a large class of 5d $\mathcal{N}=1$ superconformal field theories and show it is given by the square of the partition function on the squashed five-sphere. We show this simple relation implies a Cardy formula in 5d, which is valid in an "extended" regime in which fugacities are finite and $N$ is large. For theories with weakly coupled gravity duals we conjecture this large $N$ Cardy formula universally accounts for the microscopic entropy of spinning black holes in AdS$_{6}$. We check this explicitly for known black hole solutions in massive type IIA and type IIB string theory, carrying two angular momenta and one electric charge, and predict the entropy of black holes carrying multiple electric charges, yet to be constructed. We also discuss large $N$ properties of the $S^{3}_{b}\timesΣ_{\mathfrak{g}}$ partition function, extending previous results to theories with type IIB duals.
