Bootstrapping holographic defect correlators in N $$ \mathcal{N} $$ = 4 super Yang-Mills

Abstract

Abstract We study two-point functions of single-trace half-BPS operators in the presence of a supersymmetric Wilson line in N $$ \mathcal{N} $$ = 4 SYM. We use modern analytic bootstrap in the form of an inversion formula, that reconstructs the CFT data starting from a single discontinuity of the correlator. In the planar strong coupling limit only a finite number of conformal blocks contributes to the discontinuity, which allows us to obtain elegant closed-form expressions for two-point functions of single-trace operators O $$ \mathcal{O} $$ J of weight J = 2, 3, 4. Our bootstrap approach guarantees that the correlator satisfies all the expected properties: it has the correct discontinuity, it satisfies the superconformal Ward identities, and it has a sensible expansion in both defect and bulk OPEs. The result is also consistent with available results coming from localization. The method is completely algorithmic and can be implemented to calculate correlators of arbitrary weight.

Keywords

• Scale and Conformal Symmetries
• Wilson, ’t Hooft and Polyakov loops
• AdS-CFT Correspondence
• Supersymmetric Gauge Theory