S 2 = T 3 = ( ST ) 3 = 1 . (A1) 31 Appendix A: Group theory summary 1. A$_{4}$ representations In this appendix we summarize the main group theory properties used in the text. A$_{4}$ is the group of even permutations of four elements. It has twelve elements which can be written in terms of two generators, S and T , satisfying degenerate SU (2)$_{L}$ × SU (2)$_{R}$ bi-doublet with a very distintive phenomenology at the LHC. Hence, as the discovery of new resonances in the quark sector [33, 61], the observation of LFV processes near present limits or of new vector-like lepton doublets only decaying into taus at LHC would be a strong indication of a strongly coupled realization of EWSB. Note Added. During the writing of this paper, the possibility of new light leptonic resonances accessible at LHC has been also discussed in models with warped extra dimensions in [62, 63]. However, in our case these new resonances are a consequence of the A$_{4}$ symmetry predicting tri-bimaximal mixing, that correlates them to lepton flavor violating processes through the tau mass. A.C. thanks ITP at ETH Z¨ urich and J.S. thanks GGI for hospitality during completion and preliminary presentation of this work. This work has been partially supported by MICINN project FPA2006-05294, Junta de Andaluc´ıa projects FQM 101 and FQM03048. Acknowledgments The work of J.S. has been partially supported by SNSF under contract 200021-117873 and by a MICINN Ram´ on y Cajal contract. The work of A.C. has been supported by a MICINN FPU fellowship.