Froissart bound for/from CFT Mellin amplitudes
Parthiv Haldar, Aninda Sinha
SciPost Phys. 8, 095 (2020) · published 30 June 2020
- doi: 10.21468/SciPostPhys.8.6.095
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Abstract
We derive bounds analogous to the Froissart bound for the absorptive part of CFT$_d$ Mellin amplitudes. Invoking the AdS/CFT correspondence, these amplitudes correspond to scattering in AdS$_{d+1}$. 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 $\pi/\mu^2$, $\mu$ being the mass of the lightest exchange. For $d>4$, the form is different. We show that while for $CFT_{d\leq 6}$, the number of subtractions needed to write a dispersion relation for the Mellin amplitude is equal to 2, for $CFT_{d>6}$ the number of subtractions needed is greater than 2 and goes to infinity as $d$ goes to infinity.
Cited by 17
Authors / Affiliation: mappings to Contributors and Organizations
See all Organizations.- Department of Science and Technology, Ministry of Science and Technology (through Organization: विज्ञान एवं प्रौद्योगिकी विभाग / Department of Science and Technology [DST])
- टाटा मूलभूत अनुसंधान संस्थान / Tata Institute of Fundamental Research [TIFR]