Interpolating boundary conditions on AdS2

We consider two instances of boundary conditions for massless scalars on $AdS_2$ that interpolate between the Dirichlet and Neumann cases while preserving scale invariance. Assessing invariance under full $SL(2;\mathds{R})$ conformal group is not immediate given their non-local nature. To further clarify this issue, we compute holographically 2- 4-point correlation functions using aforementioned study transformation properties. Concretely, motivated by dual description some multi-parametric families Wilson loops in ABJM theory, look at excitations an open string around $AdS_2\subset AdS_4\times\mathbb{CP}^3$ worldsheet, thus obtaining correlators operators inserted along a $1$-dimensional defect ${\cal N}=6$ super Chern-Simons-matter theory strong coupling. Of types analyzed, only one leads to expected functional structure primaries; other exhibits covariance translations rescalings but special transformations.