  We argue that a large class of N=2 Chern-Simons-matter theories in three
dimensions have a continuous family of exact IR fixed points described by
suitable quartic superpotentials, based on holomorphy. The entire family exists
in the perturbative regime. A nontrivial check is performed by computing the
4-loop beta function of the quartic couplings, in the 't Hooft limit, with a
large number of flavors. We find that the 4-loop beta function can only deform
the family of 2-loop fixed points, and does not change the dimension of this
family. We further present an explicit computation of a perturbative correction
to the Zamolodchikov metric on this space of three-dimensional superconformal
field theories.
