Interpolating Boundary Conditions on $Ad{S}_2$

Abstract

We consider two instances of boundary conditions for massless scalars on $Ad{S}_2$ that interpolate between the Dirichlet and Neumann cases while preserving scale invariance. Assessing invariance under the full $SL(2;\mathds{R})$ 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 $Ad{S}_2\subset Ad{S}_4\times {\mathbb{CP}}^3$ 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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Cited by in corpus (5)

• Interpolating Wilson loops and enriched RG flows
• Thermal fluctuations of black holes with non-linear electrodynamics and charged Renyi entropy
• 1/3 BPS loops and defect CFTs in ABJM theory
• Wilson loops and defect RG flows in ABJM
• A network of hyperloops