  Although often chosen because of simplicity, a single scalar field does not
provide a general parametrization of an MSSM flat direction. We derive a
formalism for a class of gauge invariant polynomials which result in a
multifield description of the flat directions. In contrast to the single field
case, the vanishing of the gauge currents yields an important dynamical
constraint in the multifield framework. We consider in detail the example of
the H_uL flat direction and study the dynamical evolution during and after
inflation. We highlight the differences between the single and the multifield
flat directions. We show that in the multifield case the field space has an
intrinsic curvature and hence unsuppressed non-minimal kinetic terms for the
flat direction scalars arise. Also the phases of the individual components
non-trivially right after inflation, charging the components of the condensate
and producing an enhanced entropy after the decay of the condensate, which is
due to cross-coupling of different lepton flavours in the F term. However, the
qualitative features of the single field Affleck-Dine baryogenesis, such as the
produced total charge, remain largely unchanged.
