[@lep-ewwg]. The largest deviation has been observed in the forward-backward asymmetry of the bottom quark $A^b_{FB}$ [@Chanowitz:2001bv], whose measured value deviates by $2.9\sigma$ compared with the SM best fit prediction for the EW observables [@lep-ewwg]. On the other hand, $R_b$, the branching fraction of the $Z$ decaying to a pair of bottom quarks, is in very good agreement with the SM prediction. This leads to a challenging puzzle, with potentially new physics effects showing up in $A^b_{FB}$ but giving negligible small corrections for $R_b$. We can translate this situation in terms of the $Zb\bar b$ couplings, obtaining a small pull for $Zb_L\bar b_L$ of order $\sim\delta g^{b_L}\sim 0.003$ and a large pull for $Zb_R\bar b_R$ of order $\sim\delta g^{b_R}\sim 0.02$, compared with the SM best fit prediction [@Choudhury:2001hs] [^1].

In this work we will show that composite Higgs models can simultaneously solve the $A^b_{FB}$ anomaly and reproduce $R_b$, while giving the correct top and bottom spectrum. We will consider a four dimensional effective theory inspired by extra dimensional theories in a slice of AdS$_5$ [@Randall:1999ee]. We will adopt a two sector basis, with the elementary sector reproducing the SM massless spectrum, and the composite sector describing the first lying level 