Abstract
Two-dimensional (2d) \( \mathcal{N} \) = (4, 4) Lie superalgebras can be either “small” or “large”, meaning their R-symmetry is either \( \mathfrak{so} \)(4) or \( \mathfrak{so} \)(4) ⊕ \( \mathfrak{so} \)(4), respectively. Both cases admit a superconformal extension and fit into the one-parameter family \( \mathfrak{d} \) (2, 1; γ) ⊕ \( \mathfrak{d} \) (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 \( \mathfrak{d} \) (2, 1; γ) ⊕ \( \mathfrak{d} \) (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 \( \mathfrak{d} \) (2, 1; γ) ⊕ \( \mathfrak{d} \) (2, 1; γ). We show that a limit of these solutions, in which γ → −∞, reproduces another known class of solutions, holographically dual to small \( \mathcal{N} \) = (4, 4) superconformal defects. We then use this limit to generate new small \( \mathcal{N} \) = (4, 4) solutions with finite Ricci scalar, in contrast to the known small \( \mathcal{N} \) = (4, 4) solutions. We then use holography to compute the entanglement entropy of a spherical region centered on these small \( \mathcal{N} \) = (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 \( \mathcal{N} \) = (0, 4) surface defects through orbifolding.
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Acknowledgments
The authors would like to thank Yolanda Lozano and Nicolò Petri for useful discussions during the completion of this work and for their comments on a draft of this manuscript. The authors would also like to thank Andy O’Bannon for his contributions during the early phase of this research. The work of PC is supported by a Mayflower studentship from the University of Southampton. The work of BR is supported by the INFN. The work of BS is supported in part by the STFC consolidated grant ST/T000775/1. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics under Award Number DE-SC0024557.
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Capuozzo, P., Estes, J., Robinson, B. et al. From large to small \( \mathcal{N} \) = (4, 4) superconformal surface defects in holographic 6d SCFTs. J. High Energ. Phys. 2024, 94 (2024). https://doi.org/10.1007/JHEP08(2024)094
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DOI: https://doi.org/10.1007/JHEP08(2024)094