“Conformal Bootstrap in Mellin space”
In one of his pioneering works, Polyakov had used conformal symmetries to introduce “unitary amplitudes” that described a 4-point function. Demanding consistency of the unitary amplitude description with the OPE of a correlator, he could obtain nontrivial data of the operator spectrum. In the modern language, Polyakov’s unitary amplitudes seem to emerge from the mellin formalism of conformal field theories. A manifestly crossing symmetric mellin transform of a CFT correlator can give rise to spurious terms, not present in the OPE. Demanding the cancellation of the spurious terms lead to nontrivial information of the operators of the CFT. Using this approach, we can obtain various anomalous dimensions and OPE coefficients for both weakly coupled and strongly coupled CFTs (including new results for Wilson-Fisher point and the large spin sector).