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v3.3.3-pre
Recently there has been tremendous progress in carving out the theory space in terms of allowed regions for EFT couplings. The geometry of this space was recently characterized as a polyhedron, termed EFThedron. In this talk we will clarify the geometry in terms of the convex hull of multivariate moments, and give the complete boundary to all order in derivative expansion. For EFTs that yield permutation invariant amplitudes, we demonstrate that the geometry imposes constraint on the UV completion, in terms of bounds on the ratio of spinning spectral density, as well as the spin states in the spectrum.