Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations

Abstract

Abstract We calculate the leading contributions to the connected two-point functions of protected scalar operators in the defect version of N $$ \mathcal{N} $$ = 4 SYM theory which is dual to the D5-D3 probe-brane system with k units of background gauge field flux. This involves several types of two-point functions which are vanishing in the theory without the defect, such as two-point functions of operators of unequal conformal dimension. We furthermore exploit the operator product expansion (OPE) and the boundary operator expansion (BOE), which form the basis of the boundary conformal bootstrap equations, to extract conformal data both about the defect CFT and about N $$ \mathcal{N} $$ = 4 SYM theory without the defect. From the knowledge of the one- and two-point functions of the defect theory, we extract certain structure constants of N $$ \mathcal{N} $$ = 4 SYM theory using the (bulk) OPE and constrain certain bulk-to-boundary couplings using the BOE. The extraction of the former relies on a non-trivial, polynomial k dependence of the one-point functions, which we explicitly demonstrate. In addition, it requires the knowledge of the one-point functions of SU(2) descendant operators, which we likewise explicitly determine.

Keywords

• Boundary Quantum Field Theory
• Conformal Field Theory
• Integrable Field Theories
• Supersymmetric Gauge Theory