National Taiwan University
It has long been known that UV unitarity imposes model independent constraint in the IR in the form of positivity conditions of certain higher dimension operators. This leads to many important consequences on consistent QFTs, including the a-theorem in 4D. In this talk, I will show that these positivity constraints are merely the ``tip of the iceberg", where there's an inifinte number of non-linear qualities constraining the couplings, given by the direct product of positive geometries. This geometry cuts out the space of consistent EFTs.