Light Kaluza-Klein states in Randall-Sundrum models with custodial SU(2)

We consider Randall-Sundrum scenarios based on SU(2)L×SU(2)R and a discrete parity exchanging L with R. The custodial and parity symmetries can be used to make the tree level contribution to the T parameter and the anomalous couplings of the bottom quark to the Z very small. We show that the resulting quantum numbers typically induce a negative T parameter at one loop that, together with the positive value of the S parameter, restrict considerably these models. There are nevertheless regions of parameter space that successfully reproduce the fit to electroweak precision observables with light Kaluza-Klein excitations accessible at colliders. We consider models of gauge-Higgs unification that implement the custodial and parity symmetries and find that the electroweak data singles out a very well defined region in parameter space. In this region one typically finds light gauge boson Kaluza-Klein excitations as well as light SU(2)L singlet, and sometimes also doublet, fermionic states, that mix with the top quark, and that may yield interesting signatures at future colliders.