The discussion of the landscape of string theory vacua is often done with rather broad stroke approximations to the structures that should really be classified. For instance the landscape of flux compactifications is often done with all fluxes modeled simply as differential forms. It is known however that more properly these flux fields are really cocycles in differential cohomology (For instance the B-field is really in ordinary differential cohomology while the RR-field is really in differential K-theory). If one does take this refinement into account, then after KK-compactification what previously looked like plane scalar fields now become axion fields, which inherit periodicity from their origin in higher gauge fields. Taking this axionic nature of some of the scalar fields in string theory compactifications into account is hence known as considering the axionic landscape of string theory vacua.
Michael Dine, Guido Festuccia, John Kehayias, Weitao Wu, Axions in the Landscape and String Theory, JHEP 1101:012,2011 (arXiv:1010.4803)
Gaoyuan Wang, Thorsten Battefeld, Vacuum Selection on Axionic Landscapes, JCAP 04 (2016) 025 (arXiv:1512.04224)