  We study the Fourier-Mukai transform for holonomic D-modules on complex
abelian varieties. Among other things, we show that the cohomology support loci
of a holonomic D-module are finite unions of linear subvarieties, which go
through points of finite order for objects of geometric origin; that the
standard t-structure on the derived category of holonomic complexes
corresponds, under the Fourier-Mukai transform, to a certain perverse coherent
t-structure in the sense of Kashiwara and Arinkin-Bezrukavnikov; and that
Fourier-Mukai transforms of simple holonomic D-modules are intersection
complexes in this t-structure. This supports the conjecture that Fourier-Mukai
transforms of holonomic D-modules are "hyperk\"ahler perverse sheaves".
