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

We study strong-to-weak spontaneous symmetry breaking (SWSSB) at finite temperature and its implications in holography. SWSSB is a novel critical phenomenon that arises only in mixed states. We demonstrate SWSSB with the BTZ black hole and show that, in the bulk, it is realized through wormhole geometries connecting the two copies in the thermofield-double construction. We point out that SWSSB can be recast as an emergence of global symmetries under ensemble averaging. We further examine the interplay between SWSSB and the swampland program, and propose a new swampland conjecture for quantum-gravity theories involving ensemble averages.