Supersymmetry is generally broken by the non-vanishing vacuum energy density present during inflation. In supergravity models, such a source of supersymmetry breaking typically makes a contribution to scalar masses of order m ̃2 ∼ H2, where H2 ∼ V Mp2 is the Hubble parameter during inflation. We show that in supergravity models which possess a Heisenberg symmetry, supersymmetry breaking makes no contribution to scalar masses, leaving supersymmetric flat directions flat at tree-level. One-loop corrections in general lift the flat directions, but naturally give small negative squared masses ∼ -g2H2 (4π)2 for all flat directions that do not involve the stop. No-scale supergravity of the SU(N,1) type and the untwisted sectors from orbifold compactifications are special cases of this general set of models. We point out the importance of the preservation of flat directions for baryogenesis.
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We would like to thank Bruce Campbell for helpful conversations.T his work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Departmento f Energy under Contracts DE-FG02-94ER-40823 and DE-AC03-76SF00098,b y NSF grantsA ST-91-20005 and PHY-90-21139.