We discuss the Mellin amplitude formalism for Conformal Field Theories
(CFT's). We state the main properties of nonperturbative CFT Mellin
amplitudes: analyticity, unitarity, Polyakov conditions and polynomial
boundedness at infinity. We use Mellin space dispersion relations to
derive a family of sum rules for CFT's. These sum rules suppress the
contribution of double twist operators. We apply the Mellin sum rules
to: the epsilon-expansion and holographic CFT's.
- String Theory Seminar