$ \mathcal{N}=2 $ moduli of AdS$_{4}$ vacua: a fine-print study

International audienceWe analyze the moduli spaces near $ \mathcal{N}=4 $ supersymmetric AdS$_{4}$ vacua of string theory by combining and comparing various approaches: (a) the known exact solutions of Type IIB string theory with localized 5-brane sourcees, (b) the holographically dual 3d quiver gauge theories, (c) gauged supergravity, and (d) the representations of the superconformal algebra $ \mathfrak{o}\mathfrak{s}\mathfrak{p}\left(4\left|4\right|\right) $ . Short multiplets containing the marginal $ \mathcal{N}=2 $ deformations transform in the (2, 0), (0, 2) or (1, 1) representations of the R-symmetry group SU(2)$_{H}$ × SU(2)$_{C}$. The first two are classified by the chiral rings of the Higgs and Coulomb branches, while the latter contain mixed-branch operators. We identify the origin of these moduli in string theory, matching in particular the operators of the chiral rings with open strings on the magnetized 5-brane sources. Our results provide new evidence for the underlying holographic duality. The existence of a large number of bound-state moduli highlights the limitations of effective supergravity