In this talk, we shall look at the implications of crossing symmetry, locality, and unitarity in the UV on low-energy EFT’s. We will begin by looking at 2-2 scattering amplitudes with identical external massless scalars and massive exchanges. We will introduce a crossing symmetric dispersive representation (CSDR) of the amplitude that makes full (s,t,u)-crossing symmetry manifest, unlike the usual fixed-t dispersion relations. Though the CSDR makes crossing symmetry manifest, locality is lost and has to be restored by demanding that certain spurious singularities cancel in the low energy expansion of the amplitude leading to locality constraints.

By looking at the celestial amplitude (CA) corresponding to our original 2-2 scattering amplitude we will show that the most CA’s exhibit a novel kind of positivity, which we shall argue is related to spin-0 partial wave dominance. The locality constraints imply an infinite linear system of equations that the partial wave moments of any local theory need to satisfy. By additionally imposing linear unitarity (positivity of partial wave moments), we show that these naturally lead to the phenomenon of low-spin dominance (LSD).  Finally, we show that the crossing symmetric partial waves with spurious singularities removed, dubbed as Feynman blocks have remarkable mathematical properties that can be further used to obtain two-sided bounds on low-energy Wilson coefficients.

This is based on work with Sudip Ghosh and Aninda Sinha.