Mellin amplitudes for 1$d$ CFT

Understand

We define a Mellin amplitude for CFT$_1$ four-point functions.

• Its analytical properties are inferred from physical requirements on the correlator.
• We discuss the analytic continuation that is necessary for a fully nonperturbative definition of the Mellin transform.
• The resulting bounded, meromorphic function of a single complex variable is used to derive an infinite set of nonperturbative sum rules for CFT data of exchanged operators, which we test on known examples.