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.2 The repulsive wall structure was also found in a probe D0-brane potential in the quantum corrected geometry [6].3 Since we treat D0-branes, there is only one direction in their worldvolume: time. To form a rectangular Wilson loop, the other direction is necessary, and here we take it to be a direction in S 8 which is spanned by the scalar field of the quantum mechanics. Therefore the two separated D0-branes are located in different positions. This kind of situation was treated originally in Ref. [13]. 4 See also Refs. [15,16] for the history of the matching in the AdS/CFT. For circular Wilson loops with a totally symmetric/antisymmetric representation of SU (N ) whose dual is not a string but a D3-brane/D5brane, see Refs. [17,18].-2 -