Exact Results in Quantum Theory & Gravity

We calculate one-loop corrections to the nearly extremal black hole thermodynamics directly in the bulk. In this way, we confirm previous near-horizon calculations of the one-loop determinant. In particular, we find a family of modes that become zero modes in the extremal limit. In that limit, they localize at a finite distance from the horizon. Thus, we may interpret them as bulk counterparts of the Schwarzian modes that arise in the near-horizon geometry due to the SL(2,R) symmetry. Along the way, we explain certain confusions regarding the count of rotational zero modes (that contribute to the log corrections to the entropy).