Parafermions, brane distributions and FRW hierarchies

Abstract

I review a class of exact string backgrounds, which appear in hierarchies, where the boundary of the target space of an exact sigma model is itself the target space of another exact model. From the worldsheet viewpoint this is due to the existence of (1, 1) operators based on parafermions. From the target space side, it is reminiscent of the structure of maximally symmetric Friedmann-Robertson-Walker cosmological solutions, with broken homogeneity though. Cosmological evolution in this framework raises again the question of the nature of time in string theory.

Ricci flows and expansion in axion-dilaton cosmology

“…Clearly, this reasoning is valid under the assumption that the initial space is locally homogeneous. Exact time-dependent string backgrounds with non-homogeneous spaces exist [40,41], and there time evolution does not lead to Einstein spaces. Consistently with the above picture, in these cases, time evolution never identifies with an rg flow because it is rather related to a marginal deformation.…”