Aspects of dynamical cobordism in AdS/CFT

The cobordism conjecture implies that consistent theories of Quantum Gravity must admit the introduction of boundaries. We study the dynamical realization of the cobordism conjecture in type IIB in AdS₅ × S⁵, using the existing gravity duals of 4d 𝒩 = 4 SYM with Gaiotto-Witten superconformal boundary conditions (near-horizon limits of D3-branes ending on NS5- and D5-branes). We show that these configurations are, from the 5d perspective, dynamical cobordism solutions which start from an asymptotic AdS₅ vacuum and evolve until they hit an end of the world (ETW) brane with AdS₄ worldvolume. The latter displays localization of gravity, and provide a completion of the Karch-Randall (KR) AdS branes, in which the backreaction of running scalars replace the KR cusp in the warp factor with a smooth bump. The dynamical scalars are either in the SO(6) invariant AdS₅ bulk sector (e.g. describing the S⁵ size and its shrinking at the cobordism boundary) or brane localized (e.g. the SO(6) SO(3) × SO(3) squashing due to boundary conditions). We introduce a novel double scaling limit which zooms into the ETW brane and makes localization of gravity manifest, and which shows a tantalizing relation with wedge holography. We extend the picture to AdS₅ theories with less (super)symmetry, via orbifolds and S-folds, leading to dynamical cobordisms for gravity duals of 4d theories with 𝒩 = 2 and 𝒩 = 3 supersymmetry.