Non-Abelian coset string backgrounds from asymptotic and initial data

We describe hierarchies of exact string backgrounds obtained as non-Abelian cosets of orthogonal groups and having a space-time realization in terms of gauged WZW models. For each member in these hierarchies, the target-space backgrounds are identified with the ''boundary'' backgrounds of the next member. We explicitly demonstrate that this property holds to all orders in α′ for the three- and four-dimensional cosets, while the general structure of the backgrounds at hand suggests that the property holds in any dimension. The affiliation of the ''boundary'' theory to the ''bulk'' theory exhibits marginal operators, generically build on non-Abelian parafermion bilinears, dressed with a dilaton vertex operator. The dilaton is supported by the extra radial dimension, whose asymptotic value defines the boundary. Depending on the hierarchy, this boundary can be time-like or space-like with, in the latter case, potential cosmological applications.