Perturbative search for fixed lines in large-N gauge theories

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 Γ of the SU(4) R-symmetry, which are dual to string theory on AdS₅ × S⁵/Γ. 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. Among our examples, which include orbifolds acting freely on the S⁵, 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.