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.