  In supergravity models (such as standard superstring constructions) that
possess a Heisenberg symmetry, supersymmetry breaking by the inflationary
vacuum energy does not lift flat directions at tree level. One-loop corrections
give small squared masses that are negative (about -g^2 H^2/(4\pi)^2) for all
flat directions that do not involve the stop. After inflation, these flat
directions generate a large baryon asymmetry; typically $n_B/s \sim$ O(1). We
consider mechanisms for suppressing this asymmetry to the observed level. These
include dilution from inflaton or moduli decay, GUT nonflatness of the $vev$
direction, and higher dimensional operators in both GUT models and the MSSM. We
find that the observed BAU can easily be generated when one or more of these
effects is present.
