Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography

A bstract 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 AdS 5 . 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 ℂ 3 /ℤ ν 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 AdS 5 radius, we also obtain four-derivative corrections to the action and entropy of supersymmetric asymptotically flat black holes.