What IIB looks IIA string: string cobordisms via non-compact CFTs

A bstract The Swampland Cobordism Conjecture predicts the existence of end-of-the-world branes for every consistent Quantum Gravity theory, and domain walls connecting the Landscape. A perturbative string worldsheet description of these objects is only expected to exist when certain worldsheet invariants are vanishing or coincide across the domain wall. In this paper, we observe that many of these worldsheet obstructions can be evaded by allowing non-compact string worldsheets as part of the bordism. Using these ideas, we provide a worldsheet QFT (flowing to a critical CFT under RG flow) that connects the worldsheets of 0A and 0B string theory, as well as those of IIA and IIB string theories. The non-compact character of these interpolations means that the description of the actual domain walls develop strongly coupled regions described by a linear dilaton background, where the worldsheet description breaks down. As a result, the IIA/IIB domain wall requires strong coupling region, in agreement with effective field theory considerations. Our constructions are heavily inspired by supercritical string theory, but are logically independent from it. We also analyze the fate of IIA/IIB NS5 branes as they cross the domain wall between these two theories.