Strong-to-Weak Spontaneous Symmetry Breaking from Wormholes in Holography
ABSTRACT
Recently, the notion of symmetry has been extended to mixed states. In particular, mixed-state symmetries can be classified into two types: strong symmetries, which act on each Keldysh contour, and weak symmetries, which act on the classical average. Interestingly, strong symmetries can sometimes be spontaneously broken down to weak symmetries. This structure provides a powerful tool for understanding nonequilibrium phase transitions and hydrodynamics. Independently, over the past decades, wormholes have played an essential role in quantum gravity, especially in developing a complete understanding of the gravitational path integral. For example, they have been proposed as a possible resolution of the black hole information paradox. However, we still lack a complete and concrete understanding of such wormholes, especially in higher dimensions, since they often appear as off-shell contributions or complex saddle points as non-perturbative corrections. In this talk, we explain how statistical physics provides a useful tool for understanding wormhole physics in a concrete manner. We discuss the holographic implications of strong-to-weak symmetry breaking. In particular, we show that this phenomenon is closely related to the appearance of wormholes in AdS. We demonstrate this connection in a simple setup consisting of AdS gravity coupled to a U(1) Chern-Simons theory, and discuss that the strong-symmetry-broken phase is described by wormholes that are not solutions of the Einstein equations with the correct boundary conditions. This talk is mainly based on arXiv:2607.12022 with Masahito Yamazaki (University of Tokyo) and Kenya Tasuki (YITP), and related ongoing work.
