Higher-Derivative Corrections to the Asymptotic Virasoro Symmetry of 4d Extremal Black Holes

TL;DR

This work extends the extremal black hole/CFT framework to gravity with higher-derivative corrections by reformulating the Lagrangian with auxiliary fields to keep derivatives to second order and employing the invariant Barnich–Brandt symplectic structure for near-horizon charges. The central result is that the asymptotic Virasoro central charge, computed with the corrected charges including the boundary term E, reproduces the Iyer–Wald entropy via Cardy at the Frolov–Thorne temperature, with the leading term matching Wald entropy and all subtler terms canceling. The authors provide explicit constructions for Lagrangians without and with derivatives of the Riemann tensor, and show the cancellation persists when derivatives of the curvature are present (supported by symbolic checks up to high order). This reinforces the robustness of the extremal black hole/CFT correspondence under higher-derivative corrections and motivates further extensions to more general setups and microstate interpretations.

Abstract

We study the asymptotic Virasoro symmetry which acts on the near-horizon region of extremal four-dimensional black hole solutions of gravity theories with higher-derivative corrections, following the recently proposed Kerr/CFT correspondence. We demonstrate that its central charge correctly reproduces the entropy formula of Iyer-Wald, once the boundary terms in the symplectic structure are carefully chosen.