Description
One of the recurring themes of recent years is the appearance of deep topological structures in the study of generalized global symmetries of quantum field theories. Perhaps surprisingly, then, there is also a general expectation that in quantum gravity, there are no global symmetries at all! In modern terminology, this is an example of a "Swampland Conjecture," namely that gravity imposes non-trivial constraints on the space of consistent low energy effective field theories. In this talk we give a brief overview of these expectations both from the top down and bottom up. We then present an argument showing that completely decoupled topological quantum field theory (TQFT) sectors are incompatible with basic features of holography. In particular, we argue that the fields of any TQFT necessarily couple to gravity both non-perturbatively and perturbatively in Newton's constant.