Abstract
We consider two instances of 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 their non-local nature. To further clarify this issue, we compute holographically 2- and 4-point correlation functions using the aforementioned boundary conditions and study their transformation properties. Concretely, motivated by the dual description of some multi-parametric families of Wilson loops in ABJM theory, we look at the excitations of an open string around an AdS2 ⊂ AdS4 × ℂℙ3 worldsheet, thus obtaining correlators of operators inserted along a 1-dimensional defect in \( \mathcal{N} \) = 6 super Chern-Simons-matter theory at strong coupling. Of the two types of boundary conditions analyzed, only one leads to the expected functional structure for conformal primaries; the other exhibits covariance under translations and rescalings but not under special conformal transformations.
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Canazas Garay, A.F., Correa, D.H., Faraggi, A. et al. Interpolating boundary conditions on AdS2. J. High Energ. Phys. 2023, 146 (2023). https://doi.org/10.1007/JHEP02(2023)146
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DOI: https://doi.org/10.1007/JHEP02(2023)146