Froissart bound for/from CFT Mellin amplitudes

Abstract

We derive bounds analogous to the Froissart bound for the absorptive part of CFT_dd Mellin amplitudes. Invoking the AdS/CFT correspondence, these amplitudes correspond to scattering in AdS_{d+1}d+1. We can take a flat space limit of the corresponding bound. We find the standard Froissart-Martin bound, including the coefficient in front for d+1=4 being \pi/\mu^2π/μ2, \muμ being the mass of the lightest exchange. For d>4d>4, the form is different. We show that while for CFT_{d\leq 6}CFTd≤6, the number of subtractions needed to write a dispersion relation for the Mellin amplitude is equal to 2, for CFT_{d>6}CFTd>6 the number of subtractions needed is greater than 2 and goes to infinity as d goes to infinity.