$1/N$ correction in holographic Wilson loop from quantum gravity

Abstract

We study $1/N$ corrections to a Wilson loop in holographic duality. Extending the AdS/CFT correspondence beyond the large $N$ limit is an important but a subtle issue, as it needs quantum gravity corrections in the gravity side. To find a physical property of the quantum corrected geometry of near-horizon black 0-branes previously obtained by Hyakutake, we evaluate a Euclidean string worldsheet hanging down in the geometry, which corresponds to a rectangular Wilson loop in the $SU(N)$ quantum mechanics with 16 supercharges at a finite temperature with finite $N$. We find that the potential energy defined by the Wilson loop increases due to the $1/N$ correction, therefore the quantum gravity correction weakens the gravitational attraction.