of TeV excitations [@Contino:2006nn]. The mass eigenstates are mixtures of these sectors, with the lightest states reproducing the SM spectrum. The global symmetry of the composite sector contains the SM gauge symmetry and an extra SU(2)$_R$ global group, with SU(2)$_L\times$SU(2)$_R$ giving rise to the custodial symmetry [@custodial]. We will show that the representations under SU(2)$_R$ of the fermionic resonances associated to the third generation of quarks can be chosen to reproduce the observed $A^b_{FB}$ anomaly while preserving $R_b$, with a composite scale of order $\sim 2.7-3.4$ TeV.

The top mass, arising from the mixing between both sectors, leads to large couplings between the top and the composite sector. Since $t_L$ and $b_L$ are in the same doublet, we expect large corrections for the $b_L$ couplings. As shown in Ref. [@Agashe:2006at], the custodial symmetry can protect the $Zb_L\bar b_L$ coupling from the large corrections induced by the top mixing, resulting in very suppressed modifications of this coupling. Therefore, as noted in Ref. [@Bouchart:2008vp], in the minimal scenario it is in general not possible to obtain the proper shift for $Zb_L\bar b_L$. Moreover, the large correction for $Zb_R\bar b_R$ is in conflict with the bottom mass, since rather strong interactions between the 