Gauge/Gravity Duality for Interactions of Spherical Membranes in 11-dimensional pp-wave

TL;DR

This paper demonstrates a precise match between supergravity and gauge theory calculations for the interaction potential of spherical membranes in an 11-dimensional pp-wave background, validating gauge/gravity duality in this context.

Contribution

It provides the first detailed comparison of membrane interactions in supergravity and the BMN matrix model, including the full interpolation between membrane and graviton regimes.

Findings

Exact agreement between supergravity and gauge theory potentials.

Effective potential valid beyond small-separation approximation.

Full interpolation between membrane and graviton interactions.

Abstract

We investigate the gauge/gravity duality in the interaction between two spherical membranes in the 11-dimensional pp-wave background. On the supergravity side, we find the solution to the field equations at locations close to a spherical source membrane, and use it to obtain the light cone Lagrangian of a spherical probe membrane very close to the source, i.e., with their separation much smaller than their radii. On the gauge theory side, using the BMN matrix model, we compute the one-loop effective potential between two membrane fuzzy spheres. Perfect agreement is found between the two sides. Moreover, the one-loop effective potential we obtain on the gauge theory side is valid beyond the small-separation approximation, giving the full interpolation between interactions of membrane-like objects and that of graviton-like objects.