Much of the recent work on bootstrapping EFT amplitudes utilizes the positivity of the imaginary part of the partial wave amplitudes. However from unitarity, these partial wave amplitudes are also bounded from above. In this lecture I will talk about how to introduce this feature by viewing the bootstrap as a geometric problem. The result will be an ``upper bound" on each Wilson coefficient weighted by the cutoff. This result will come in handy when we consider fluctuations around a null background at low energies, where the effects of higher derivative terms will contribute and can be consistently taken into account. The absence of super-luminal modes will introduce new constraints to the EFT at hand.
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