From Large to Small N=(4,4) Superconformal Surface Defects in Holographic 6d SCFTs

Two-dimensional (2d) N=(4,4) Lie superalgebras can be either "small" or "large", meaning their R-symmetry is either so(4) or so(4) ⊕ so(4), respectively. Both cases admit a superconformal extension and fit into the one-parameter family d(2,1;γ)⊕ 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 d(2,1;γ)⊕ 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 d(2,1;γ)⊕ 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 N=(4,4) superconformal defects. We then use this limit to generate new small N=(4,4) solutions with finite Ricci scalar, in contrast to the known small N=(4,4) solutions. We then use holography to compute the entanglement entropy of a spherical region centered on these small 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 N=(0,4) surface defects through orbifolding.