Abstract
We compute the supersymmetric Rényi entropies across a spherical entanglement surface in \( \mathcal{N}=4 \) SU(N) SYM theory using localization on the four-dimensional ellipsoid. We extract the leading result at large N and λ and match its universal part to a gravity calculation involving a hyperbolically sliced supersymmetric black hole solution of \( \mathcal{N}={4}^{+} \) SU(2) × U(1) gauged supergravity in five dimensions. We repeat the analysis in the presence of a Wilson loop insertion and find again a perfect match with the dual string theory. Understanding the Wilson loop operator requires knowledge of the full ten-dimensional IIB supergravity solution which we elaborate upon.
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ArXiv ePrint: 1409.0542
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Crossley, M., Dyer, E. & Sonner, J. Super-Rényi entropy & Wilson loops for \( \mathcal{N}=4 \) SYM and their gravity duals. J. High Energ. Phys. 2014, 1 (2014). https://doi.org/10.1007/JHEP12(2014)001
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DOI: https://doi.org/10.1007/JHEP12(2014)001