Superconformal partial waves for stress-tensor multiplet correlator in 4D N $$ \mathcal{N} $$ = 2 SCFTs

Abstract

Abstract We compute the superconformal partial waves of the four-point correlator 〈JJJJ〉, in which the external operator J is the superconformal primary of the 4D N $$ \mathcal{N} $$ = 2 stress-tensor multiplet J $$ \mathcal{J} $$ . We develop the superembedding formalism for the superconformal field theories (SCFTs) with extended supersymmetry. In N $$ \mathcal{N} $$ = 2 SCFTs, the three- point functions JJO $$ \left\langle \mathcal{JJO}\right\rangle $$ with general multiplet O $$ \mathcal{O} $$ contain two independent nilpotent superconformal invariants and new superconformal tensor structures, which can be nicely constructed from variables in superembedding space, and the three-point functions can be written in compact forms. We compute the superconformal partial waves corresponding to the exchange of long multiplets using supershadow approach. The results are consistent with the non-trivial constraints by decomposing the N $$ \mathcal{N} $$ = 2 superconformal blocks into N $$ \mathcal{N} $$ = 1 superconformal blocks. Our results provide the necessary ingredient to study the fascinating 4D N $$ \mathcal{N} $$ = 2 SCFTs using conformal bootstrap.

Keywords

• Conformal Field Theory
• Extended Supersymmetry
• Superspaces
• Supersym- metric Gauge Theory