Abstract
A Cardy-like regime of the four-dimensional superconformal index has been shown to be governed by ’t Hooft anomalies and to single out a large-N saddle carrying the Bekenstein-Hawking entropy of dual supersymmetric black holes in AdS5. For the universal index where no flavour fugacities are turned on, this correspondence has been improved by matching the first subleading corrections to the saddle-point action with the four-derivative corrections to the black hole action in minimal gauged supergravity, as well as the respective corrected entropies. Here, we extend this match by including flavour symmetries. We consider five-dimensional gauged supergravity with vector multiplet and four-derivative couplings, and provide an effective theory reproducing the ’t Hooft anomalies of the R- and flavour symmetries of generic holographic superconformal field theories at next-to-leading order in the large-N expansion. Then we focus on a specific model dual to ℂ3/ℤν quiver gauge theories, where the ’t Hooft anomaly coefficients receive simple but sufficiently generic corrections. In this model, we evaluate the four-derivative corrections to the on-shell action of the supersymmetric multi-charge black hole, showing agreement with the flavoured Cardy-like formula from the index. We give a prediction for the corrected entropy of the supersymmetric black hole and discuss the general validity of our results. Taking the limit of infinite AdS5 radius, we also obtain four-derivative corrections to the action and entropy of supersymmetric asymptotically flat black holes.
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Acknowledgments
We would like to thank Marina David, Kiril Hristov, Noppadol Mekareeya, Mehmet Ozkan, Gabriele Tartaglino-Mazzucchelli, Sameer Murthy, Dan Waldram and Alberto Zaffaroni for discussions. DC is supported in part by the MUR-PRIN contract 2022YZ5BA2 — Effective quantum gravity. AR is supported by a postdoctoral fellowship associated to the MIUR-PRIN contract 2020KR4KN2 — String Theory as a bridge between Gauge Theories and Quantum Gravity, and partially by the INFN Sezione di Roma “Tor Vergata”. AR further thanks the GSS group at the University of Padova for hospitality and the INFN Sezione di Padova for financial support.
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Cassani, D., Ruipérez, A. & Turetta, E. Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography. J. High Energ. Phys. 2024, 276 (2024). https://doi.org/10.1007/JHEP05(2024)276
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DOI: https://doi.org/10.1007/JHEP05(2024)276