From large to small N = (4, 4) superconformal surface defects in holographic 6d SCFTs

A bstract Two-dimensional (2d) N N = (4, 4) Lie superalgebras can be either “small” or “large”, meaning their R-symmetry is either so so (4) or so so (4) ⊕ so so (4), respectively. Both cases admit a superconformal extension and fit into the one-parameter family d d (2 , 1; γ ) ⊕ 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 d d (2 , 1; γ ) ⊕ d d (2 , 1; γ ) that are asymptotically locally AdS 7 ×𝕊 4 . These solutions are holographically dual to the 6d maximally superconformal field theory with 2d superconformal defects invariant under d d (2 , 1; γ ) ⊕ 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 N N = (4, 4) superconformal defects. We then use this limit to generate new small N N = (4, 4) solutions with finite Ricci scalar, in contrast to the known small N N = (4, 4) solutions. We then use holography to compute the entanglement entropy of a spherical region centered on these small 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 N N = (0 , 4) surface defects through orbifolding.