Beta functions for double-trace couplings in orbifold gauge theories

We summarize calculation of one-loop beta functions in orbifolds of the script = 4 SYM theory by a discrete subgroup Γ of the SU(4) R-symmetry, which are dual to string theory on AdS₅ × S⁶/ Γ, and the general strategy for determining whether there is a fixed line passing through the origin of the coupling constant space. We emphasize the importance of decoupling the U(1) factors. We describe a class of non-supersymmetric field theories corresponding to orbifolds acting freely on the S⁵ which preserve some of its global symmetries. In this class 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 AdS₅ × S⁵/Γ is discussed.