Generalized additivity in unitary conformal field theories

It was demonstrated in [2] and [12] that d=4d=4 unitary CFT's satisfy a special property: if a scalar operator with conformal dimension Δ exists in the operator spectrum, then the conformal bootstrap demands that large spin primary operators have to exist in the operator spectrum of the CFT with a conformal twist close to 2Δ+2N2Δ+2N for any integer N. In this paper the conformal bootstrap methods in [1] that were used to find the anomalous dimension of the N=0N=0 operators have been generalized to recursively find the anomalous dimension of all large spin operators of this class. In AdS these operators can be interpreted as the excited states of the product states of objects that were found in other works.