The most general 4 D $$ \mathcal{D} $$ N $$ \mathcal{N} $$ = 1 superconformal blocks for scalar operators

Abstract

We compute the most general superconformal blocks for scalar operators in 4 $$ \mathcal{D} $$ $$ \mathcal{N} $$ = 1 superconformal field theories. Specifically we employ the supershadow formalism to study the four-point correlator 〈Φ1Φ2Φ3Φ4〉, in which the four scalars, Φ i , have arbitrary scaling dimensions and R-charges. The only constraint on the R-charges is from R-symmetry invariance of the four-point correlator and the exchanged operators can have arbitrary R-charges. Our results extend previous studies on 4 $$ \mathcal{D} $$ $$ \mathcal{N} $$ = 1 superconformal blocks to the most general case, which are the essential ingredient for bootstrapping mixed correlators of scalars with independent scaling dimensions and R-charges.