# PU High Energy Theory Seminar

## Wormholes and Factorization in Exact Effective Theory

** Abstract:** I will discuss the general framework of effective theories obtained via exact path integration of a complete theory over some sector of its degrees of freedom.Theories constructed this way contain multi-integrals which couple fields arbitrarily far apart. In certain settings these couplings connect path-disconnected components of the space, in which case I dub them quantum wormholes.

Any state the path integral of such an effective theory prepares is shown to be a partial trace of a state of the complete theory over the integrated-out sector. The resulting reduced density operator is generally mixed due to bra-ket wormholes. An infinite family of ensembles of pure states of the complete theory giving the same effective state is identified. These allow one to equivalently interpret any effective state as being prepared by an ensemble of theories. When computing entropic quantities, bra-ket wormholes give rise to replica wormholes. This causes replica path integrals for the effective theory to not factorize even when the underlying manifold does, as expected from mixing. In contrast, effective theories obtained by derivative expansions have no quantum wormholes and prepare pure states. There exist operators in the algebra of effective theories which can distinguish mixed from pure states, implying a breakdown of non-exact effective theories for sufficiently complex observables.

If time allows, I will also address how this framework unifies and provides new insights into much of the phenomena observed in quantum gravity, including the interplay between wormholes and unitarity, the breakdown of bulk effective theory, the factorization puzzle, state ensembles, theory ensembles, quantum error correction, and baby universes.

Based on 2404.10035.