Duality origami: Emergent ensemble symmetries in holography and Swampland

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.