Interpolating Boundary Conditions on $AdS_2$

CANAZAS GARAY, ANTHONY; CORREA, DIEGO H.; FARAGGI, ALBERTO; SILVA, GUILLERMO A.

JOURNAL OF HIGH ENERGY PHYSICS - (Online)

Springer

Año: 2023 vol. 2023

1029-8479

We consider two instances of boundary conditions for massless scalars on AdS2 thatinterpolate between the Dirichlet and Neumann cases while preserving scale invariance. Assessinginvariance under the full SL(2; R) conformal group is not immediate given their non-local nature. Tofurther clarify this issue, we compute holographically 2- and 4-point correlation functions using theaforementioned boundary conditions and study their transformation properties. Concretely, motivatedby the dual description of some multi-parametric families of Wilson loops in ABJM theory, we lookat the excitations of an open string around an AdS2 ⊂ AdS4 × CP3 worldsheet, thus obtainingcorrelators of operators inserted along a 1-dimensional defect in N = 6 super Chern-Simons-mattertheory at strong coupling. Of the two types of boundary conditions analyzed, only one leads to theexpected functional structure for conformal primaries; the other exhibits covariance under translationsand rescalings but not under special conformal transformations.