From large to small $$ \mathcal{N} $$ = (4, 4) superconformal surface defects in holographic 6d SCFTs

Abstract

Abstract Two-dimensional (2d) $$ \mathcal{N} $$ N = (4, 4) Lie superalgebras can be either “small” or “large”, meaning their R-symmetry is either $$ \mathfrak{so} $$ so (4) or $$ \mathfrak{so} $$ so (4) ⊕ $$ \mathfrak{so} $$ so (4), respectively. Both cases admit a superconformal extension and fit into the one-parameter family $$ \mathfrak{d} $$ d (2, 1; γ) ⊕ $$ \mathfrak{d} $$ d (2, 1; γ), with parameter γ ∈ (−∞, ∞). The large algebra corresponds to generic values of γ, while the small case corresponds to a degeneration limit with γ → −∞. In 11d supergravity, we study known solutions with superisometry algebra $$ \mathfrak{d} $$ d (2, 1; γ) ⊕ $$ \mathfrak{d} $$ d (2, 1; γ) that are asymptotically locally AdS7×𝕊4. These solutions are holographically dual to the 6d maximally superconformal field theory with 2d superconformal defects invariant under $$ \mathfrak{d} $$ d (2, 1; γ) ⊕ $$ \mathfrak{d} $$ d (2, 1; γ). We show that a limit of these solutions, in which γ → −∞, reproduces another known class of solutions, holographically dual to small$$ \mathcal{N} $$ N = (4, 4) superconformal defects. We then use this limit to generate new small $$ \mathcal{N} $$ N = (4, 4) solutions with finite Ricci scalar, in contrast to the known small $$ \mathcal{N} $$ N = (4, 4) solutions. We then use holography to compute the entanglement entropy of a spherical region centered on these small $$ \mathcal{N} $$ N = (4, 4) defects, which provides a linear combination of defect Weyl anomaly coefficients that characterizes the number of defect-localized degrees of freedom. We also comment on the generalization of our results to include $$ \mathcal{N} $$ N = (0, 4) surface defects through orbifolding.