Realization of de Sitter spacetime in AdS/CFT

We construct horizonless, everywhere-regular solitons containing a de~Sitter core inside an asymptotically anti–de~Sitter spacetime, using an ordinary action of Einstein gravity, a Maxwell field, and a charged scalar. The object is a gravitating gauged $Q$-ball whose false-vacuum interior acts as a positive effective cosmological constant, sourcing an inner de~Sitter region joined through a thin wall to a charged, asymptotically AdS exterior. Two general requirements are emphasized: the scalar must lie in a near-false-vacuum (slow-roll–like) regime, and the exterior is driven to the extremal Reissner–Nordström–AdS locus in the thin-wall limit, in which the wall approaches the common would-be horizon. Since the solution is static and spherically symmetric, it may correspond to a semiclassical charge-$Q$ state of the dual CFT, realizing de~Sitter space approximately within a holographic theory. We also discuss free fluctuations whose de~Sitter–core modes appear as parametrically low-lying excitations above the state, bulk reconstruction, and the near-extremal regime, where finite-$\mathcal{N}$ effects are expected to cut off the formal classical throat and replace its independent free-field modes by an interacting near-throat sector.