4D Conformal Field Theories and Strings on Orbifolds

We propose and test correspondences between 4D quantum field theories (QFTs) with $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2,1,0$ (super)conformal invariance and type IIB string theory on various orbifolds of ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$. This allows us to translate the problem of finding stable nontrivial nonsupersymmetric string backgrounds into the problem of realizing nontrivial renormalization group (RG) fixed point QFTs on branes. RG fixed lines in this context correspond to string theories in which no vacuum energy is generated quantum mechanically.