HET Journal club: Kasper Vardinghus
Speaker: Kasper Vardinghus
Title: Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations
Abstract: We calculate the leading quantum contributions to the connected two-point functions of protected scalar operators in the defect version of 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=4 SYM theory without the defect. From the knowledge of the one- and two-point functions of the defect theory, we are able to extract the bulk-to-boundary couplings using the BOE and certain structure constants of N=4 SYM theory using the (bulk) OPE. The extraction of the latter 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.