Emergent closed universes in symmetric orbifold CFTs

A bstract We identify sectors in large N symmetric orbifold CFTs, whose properties are similar to those of closed universes. Starting from tensor product states built out of a finite dimensional low energy subspace of the seed theory, we show that the large N Hilbert space decomposes into superselection sectors labeled by occupation number distributions. Before imposing the orbifold gauge constraint, these sectors have exponentially large dimensions, and the maximally entropic sector dominates the ungauged Hilbert space. We argue that this sector exhibits several characteristic features expected of a closed universe Hilbert space: product states become indistinguishable from a mixed state at the level of simple correlators, and the associated operator algebra is naturally a hyperfinite type II 1 von Neumann algebra. We then impose the S N gauge constraint. The large gauge redundancy drastically reduces the number of independent states. In particular, in the large N limit, the dimension of the physical Hilbert space grows only polynomially with N . Consequently, each superselection sector after imposing the constraint is one dimensional in this limit. This is qualitatively similar to the behavior suggested by gravitational path integral calculations with wormholes. Within this proposed closed universe interpretation, we show why, in this setup, the Hartle-Hawking type semiclassical approximation for the dominant closed universe fails to reproduce the CFT results. Nevertheless, the dominant saddle point approximation for gravitational path integral calculation may be reconstructed once the CFT degrees of freedom are coupled to external observer degrees of freedom.