Symmetric product orbifold universality and the mirage of an emergent spacetime

We study thermal two-point functions and four-point functions involving two heavy twisted operators and two light probes in symmetric product orbifolds. We identify cases where they are universal at large N, that is, they are only sensitive to the orbifold structure. Surprisingly, such observables mimic correlators obtained from the BTZ background, even though symmetric product orbifolds are not dual to semi-classical gravity. We discuss the interpretation of these results in light of the criteria for emergence of spacetime via Von Neumann algebras. Our analysis implies that a condition on the infinite N thermal two-point functions cannot be stringent enough to define an emergent spacetime and the concept of a sharp horizon.