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

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.

arXiv comment34 pages

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Cited by in corpus (9)

• pp Wave Big Bangs: Matrix Strings and Shrinking Fuzzy Spheres
• 1/2 BPS Geometries of M2 Giant Gravitons
• Dynamics of Antimembranes in the Maximally Supersymmetric Eleven-Dimensional pp Wave
• Smearing Effect in Plane-Wave Matrix Model
• Point-Like Graviton Scattering in Plane-Wave Matrix Model
• Emergence of the fuzzy horizon through gravitational collapse
• Graviton and Spherical Graviton Potentials in Plane-Wave Matrix Model - overview and perspective -
• Probing Smearing Effect by Point-Like Graviton in Plane-Wave Matrix Model
• Emergent geometry through quantum entanglement in Matrix theories