de Sitter Vacua & pUniverses

We analyze a simple extension of the Schwinger model, which we refer to as the $p$-Schwinger model, on a de Sitter background. In this theory, the charged massless fermions carry non-unit integer charge $p$. In Minkowski space, the $p$-Schwinger model has discrete zero- and one-form global symmetries that are spontaneously broken, yielding $p$ degenerate ground states. We demonstrate that these features persist upon placing the $p$-Schwinger model on a global de Sitter background, establishing that such discrete global symmetries can be spontaneously broken for quantum field theories in de Sitter space. In particular, the theory is endowed with $p$ distinct, but locally-indistinguishable, de Sitter invariant states, the de Sitter vacua, satisfying the Hadamard property. We couple a variant of the $p$-Schwinger model with ${\rm N}_{\rm f}$ flavors to quantum gravity with $\Lambda>0$, and demonstrate the existence of a semiclassical de Sitter saddle at large ${\rm N}_{\rm f}$. In the gravitational theory, the $p$ de Sitter invariant vacua are speculatively interpreted as microstates of the de Sitter horizon in the low-energy effective field theory.