A One-Loop Test of Quantum Supergravity
Sayantani Bhattacharyya, Alba Grassi, Marcos Marino, Ashoke Sen
TL;DR
The paper tests the universal logarithmic correction seen in the large‑N ABJM-like CFT partition functions by performing a macroscopic one‑loop calculation in eleven-dimensional supergravity on AdS4×X7. In odd dimensions, the log term arises only from zero modes, here from a two‑form ghost, leading to a simple coefficient determined by the zero‑mode measure. The result $\Delta F = -\tfrac{3}{2} \log L$, exactly matching the microscopic CFT prediction and supporting AdS/CFT at next‑to‑leading order in 1/N with universality across X7. This strengthens the bridge between microscopic gauge theory results and macroscopic quantum gravity, and suggests extensions to related AdS backgrounds and string reductions.
Abstract
The partition function on the three-sphere of ABJM theory and its generalizations has, at large N, a universal, subleading logarithmic term. Inspired by the success of one-loop quantum gravity for computing the logarithmic corrections to black hole entropy, we try to reproduce this universal term by a one-loop calculation in Euclidean eleven-dimensional supergravity on AdS_4 \times X_7. We find perfect agreement between the results of ABJM theory and the eleven dimensional supergravity.