Analyticity and unitarity's offspring: anomalous dimensions and the space of EFTs

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In the first part of the talk I will present how to compute anomalous dimensions of EFT operators using on-shell scattering amplitudes. The method is used to compute some two loop transitions, which are important to provide a complete characterisation of the dynamics affecting some low energy precision experiments. In the second part, I show how unitarity, analycity and locality impose stringent non-trivial constraints to the space of possible EFTs, invisible at the Lagrangian level by only considering the symmetries of the IR theory.