  The logarithmic running of marginal double-trace operators is a general
feature of 4-d field theories containing scalar fields in the adjoint or
bifundamental representation. Such operators provide leading contributions in
the large N limit; therefore, the leading terms in their beta functions must
vanish for a theory to be large N conformal. We calculate the one-loop beta
functions in orbifolds of the N=4 SYM theory by a discrete subgroup Gamma of
the SU(4) R-symmetry, which are dual to string theory on AdS_5 x S^5/Gamma. We
present a general strategy for determining whether there is a fixed line
passing through the origin of the coupling constant space. Then we study in
detail some classes of non-supersymmetric orbifold theories, and emphasize the
importance of decoupling the U(1) factors. Among our examples, which include
orbifolds acting freely on the S^5, we do not find any large N
non-supersymmetric theories with fixed lines passing through the origin.
Connection of these results with closed string tachyon condensation in AdS_5 x
S^5/Gamma is discussed.
