Unitarity and Causality constraints on Effective Field Theories

In this PhD dissertation, we discuss constraints on Effective Field Theories (EFTs) from the requirement of Lorentz invariance, Unitarity, Causality and polynomially boundedness of the underlying UV completion. After a short review of the analyticity properties of the S-matrix, we go beyond the familiar positivity bounds, deriving a new class of inequalities that any low-energy theory must satisfy, in order to admit a consistent UV completion. We apply these bounds to dRGT massive gravity, showing that their combination with the experimental constraints on the graviton mass implies that the true cutoff is of order solar system distances, making this theory unable to describe gravitational phenomena. We construct EFTs of generic integer higher spin (HS) particles in flat spacetime, providing a novel way to power-count the interactions and a generalisation of the equivalence theorem to HS theories. We also discuss the consequences of the beyond positivity bounds, finding that for high values of the spin ($sgeq 2$), either the theory is extremely weakly coupled or there is no separation between the mass of these particles and the true cutoff. In the last Chapter, we discuss a novel paradigm of fermion compositeness consistent with the positivity bounds: goldstino-compositeness. We construct the effective theory of $mathcal{N}$ Goldstini and show how the Standard Model (SM) can emerge from this dynamics. In particular, we discuss the possibility that the SM fermions arise from a spontaneously broken supersymmetric sector as (pseudo)Goldstini. We derive bounds on this kind of compositeness, for quarks and leptons, using dilepton searches at LEP, dijets at the LHC. We find that a scale of compositeness for Goldstino-like electrons in the 2 TeV range is compatible with present data, and so are Goldstino-like first generation quarks with a compositeness scale in the 10 TeV range.