In supergravity models (such as standard superstring constructions) that po
ssess a Heisenberg symmetry, supersymmetry breaking by the inflationary vac
uum energy does not lift flat directions at tree-level, One-loop correction
s give small squared masses that are negative (similar to-g(2)H(2)/(4 pi)(2
)) for all flat directions that do not involve the stop, After inflation, t
hese flat directions generate a large baryon asymmetry; typically n(B)/s si
milar to O(1), We consider mechanisms for suppressing this asymmetry to the
observed level. These include dilution from inflaton or moduli decay, GUT
non-flatness of the vev direction, and higher dimensional operators in both
GUT models and the MSSM. We find that the observed BAU can easily be gener
ated when one or more of these effects is present. (C) 1999 Elsevier Scienc
e B.V.