  We introduce a simple, exactly solvable strong-randomness renormalization
group (RG) model for the many-body localization (MBL) transition in one
dimension. Our approach relies on a family of RG flows parametrized by the
asymmetry between thermal and localized phases. We identify the physical MBL
transition in the limit of maximal asymmetry, reflecting the instability of MBL
against rare thermal inclusions. We find a critical point that is localized
with power-law distributed thermal inclusions. The typical size of critical
inclusions remains finite at the transition, while the average size is
logarithmically diverging. We propose a two-parameter scaling theory for the
many-body localization transition that falls into the Kosterlitz-Thouless
universality class, with the MBL phase corresponding to a stable line of fixed
points with multifractal behavior.
