  As famously observed by Ooguri and Vafa nearly twenty years ago, scalar field
moduli spaces in quantum gravity appear to exhibit various universal features.
For instance, they seem to be infinite in diameter, have trivial fundamental
group, and feature towers of massive particles that become light in their
asymptotic limits. In this essay, we explain how these features can be
reformulated in more modern language using generalized notions of global
symmetries. Such symmetries are ubiquitous in non-gravitational quantum field
theories, but it is widely believed that they must be either gauged or broken
in quantum gravity. In what follows, we will see that the observations of
Ooguri and Vafa can be understood as consequences of such gauging or breaking.
