Abstract
For a conformal theory it is natural to seek the conformal
moduli space, 
c to which it belongs, generated by the exactly
marginal deformations. By now we should have the tools to determine
c in the presence of enough supersymmetry. Here it is shown that
its dimension is determined in terms of a certain index. Moreover, the
D-term of the global group is an obstruction for deformation, in
presence of a certain amount of preserved supersymmetry. As an example
we find that the deformations of the membrane (3d) field theory, under
certain conditions, are in 35/SL(4,
). Other
properties including the local geometry of c are discussed.
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