Abstract
We exhibit an infinite family of supersymmetric phases in the three-dimensional ABJM superconformal field theory and the dual asymptotically AdS4 gravity. They are interpreted as partially deconfined phases which generalize the confined/pure AdS phase and deconfined/supersymmetric black hole phase. Our analysis involves finding a family of saddle-points of the superconformal index labelled by rational points (equivalently, roots of unity), separately in the bulk and boundary theories. In the ABJM theory we calculate the free energy of each saddle by the large-N asymptotic expansion of the superconformal index to all orders in perturbation theory near the saddle-point. We find that this expansion terminates at finite order. In the gravitational theory we show that there is a corresponding family of solutions, constructed by orbifolding the eleven-dimensional uplift of the supersymmetric black hole. The on-shell gravitational action of each orbifold agrees with the free energy of the corresponding saddle in the SCFT. We find that there are two saddles in the ABJM theory with the same entropy as the supersymmetric black hole, corresponding to the two primitive fourth-roots of unity, which causes macroscopic oscillations in the microcanonical index.
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Acknowledgments
We are grateful to Arash Arabi Ardehali, Davide Cassani, Zohar Komargodski, Dario Martelli, Luigi Tizzano, Chiara Toldo, and Alberto Zaffaroni for helpful discussions. We would also like to thank the organizers and participants of the SCGP workshop “Supersymmetric Black Holes, Holography and Microstate Counting” for many interesting comments and discussions. This work is supported by the ERC Consolidator Grant N. 681908, “Quantum black holes: A macroscopic window into the microstructure of gravity”, and by the STFC grants ST/P000258/1 and ST/T000759/1. ACB acknowledges financial support from the INFN grant GSS (Gauge Theories, Strings and Supergravity). PBG gratefully acknowledges support from the Simons Center for Geometry and Physics, Stony Brook University, at which some of the research for this paper was performed.
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Genolini, P.B., Cabo-Bizet, A. & Murthy, S. Supersymmetric phases of AdS4/CFT3. J. High Energ. Phys. 2023, 125 (2023). https://doi.org/10.1007/JHEP06(2023)125
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DOI: https://doi.org/10.1007/JHEP06(2023)125