We discuss the interrelations between several ideas in quantum gravity – holography, the Swampland, and the concept of ensemble averaging. To do so, we study ensemble averages of Narain-type theories associated with general even quadratic forms and their holographic duals. We establish the emergence of global symmetries and discuss their consistency with conjectures forbidding such symmetries. We also discuss how the spectral decomposition of Narain partition functions suggests a natural embedding of ensemble averaging within the low-energy limit of certain string compactifications, which in turn allows a connection with the Swampland program.

中文翻译：

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二元性折纸：全息术和沼泽地中的新兴集合对称性


我们讨论了量子引力中几个概念之间的相互关系——全息术、沼泽地和集成平均的概念。为此，我们研究了与一般偶次形式及其全息对偶相关的 Narain 型理论的集合平均值。我们建立了全局对称性的出现，并讨论了它们与禁止这种对称性的猜想的一致性。我们还讨论了 Narain 分区函数的频谱分解如何表明在某些字符串压缩的低能量限制内自然嵌入集成平均，这反过来又允许与 Swampland 程序连接。