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

Abstract

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 AdS_7 × S^4. 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.

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Identifiers

ORCID for Pietro Capuozzo: orcid.org/0000-0002-6486-9923

ORCID for Benjamin Suzzoni: orcid.org/0000-0002-3941-0256

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