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Chiral low-energy physics from squashed branes in deformed ${\cal N}=4$ SYM

We discuss the low-energy physics which arises on stacks of squashed brane solutions of $SU(N)$ ${\cal N}=4$ SYM, deformed by a cubic soft SUSY breaking potential. A brane configuration is found which leads to a low-energy physics similar to the standard model in the broken phase, assuming suitable VEV's of the scalar zero modes. Due to the triple self-intersection of the branes, the matter content includes that of the MSSM with precisely 3 generations and right-handed neutrinos. No exotic quantum numbers arise, however there are extra chiral superfields with the quantum numbers of the Higgs doublets, the $W,Z$, $e_R$ and $u_R$, whose fate depends on the details of the rich Higgs sector. The chiral low-energy sector is complemented by a heavy mirror sector with the opposite chiralities, as well as super-massive Kaluza-Klein towers completing the ${\cal N}=4$ multiplets. The sectors are protected by two gauged global $U(1)$ symmetries.