Interpolating Boundary Conditions on AdS2

Abstract

We consider boundary conditions for massless scalars on AdS2 that interpolate between the Dirichlet and Neumann cases while preserving scale invariance. Assessing invariance under the full SL(2; R) conformal group is not immediate given the non-local nature of the boundary conditions. To further understand this issue, we compute the holographic 2- and 4-point correlation functions using the interpolating boundary conditions and study their transformation properties. Concretely, we look at the fluctuations of an open string around an AdS2 ⊂ AdS4 × CP3 worldsheet and identify the scalar field with one of the fluctuations in CP3 , thus obtaining correlators of excitations inserted along a 1-dimensional defect in N = 6 super Chern-Simons-matter theory at strong coupling. Of the two types of boundary conditions discussed, only one leads to a functional structure expected for correlators of conformal primaries; the other exhibits covariance under translations and rescalings but not special conformal transformations.