Strong-to-Weak Spontaneous Symmetry Breaking from Wormholes in Holography

The authors investigate the nature of strong-to-weak spontaneous symmetry breaking (SWSSB), a phenomenon occurring in mixed quantum states where a strong symmetry (which acts on the density matrix as a phase) is broken down to a weak symmetry (which leaves the density matrix invariant). The study explores how this abstract quantum information concept manifests in holographic gravity duals and its broader implications for the Swampland program.

The researchers utilize the AdS/CFT correspondence to study SWSSB at finite temperature. They model the mixed state using the thermofield-double construction and compute Rènyi-2 and Wightman correlators. By implementing charge projection operators as Wilson lines in the bulk, they analyze the connectivity of the gravitational path integral. They further connect this to the concept of ensemble averaging, where weak symmetries emerge from the averaging of non-symmetric configurations.

• The authors demonstrate that SWSSB is realized in the bulk through wormhole geometries that connect the two boundaries of the thermofield-double state. This provides a geometric interpretation of long-range order in the Schwinger-Keldysh path integral.
• They show that the non-vanishing of Rènyi-2 and Wightman correlators in the large-distance limit serves as a diagnostic for these wormholes.
• The study proposes a new "Swampland SWSSB Conjecture," which posits that in any theory of quantum gravity, a strong global symmetry of a mixed state must be broken at least down to a weak symmetry, effectively constraining the allowed configurations of quantum gravity theories.

This work bridges the gap between quantum information theory, non-equilibrium statistical mechanics, and quantum gravity. By linking the breaking of symmetries in mixed states to the existence of wormholes, it provides a new tool for probing the structure of spacetime and the consistency of quantum gravity theories, particularly those involving ensemble averages.