Gauge coupling unification and doublet-triplet splitting via GUT dynamical breaking

An interesting framework to achieve gauge coupling unification consists in adding to the Standard Model Lagrangian non-renormalizable operators of $d \geq 5$, which affect the kinetic term of gauge fields. We first review the phenomenology related to this framework in the context of $SU(5)$, identifying which are the most interesting representations for the sake of achieving coupling unification. Secondly, we point out that in the case of a dynamical breaking pattern, it is possible to relate gauge coupling unification with the doublet-triplet splitting problem. We show that condensates of fermions in the $5$ representation do not lead to viable models because of proton decay constraints. At difference, we point out that successful models can be obtained by considering condensates of fermions in the $10$, as well as in the $24$ representations.