A Monte-Carlo study of the AdS/CFT correspondence: an exploration of quantum gravity effects

Abstract

In this paper we study the AdS/CFT correspondence for N=4 SYM with gauge group U(N), compactified on S^3 in four dimensions using Monte-Carlo techniques. The simulation is based on a particular reduction of degrees of freedom to commuting matrices of constant fields, and in particular, we can write the wave functions of these degrees of freedom exactly. The square of the wave function is equivalent to a probability density for a Boltzman gas of interacting particles in six dimensions. From the simulation we can extract the density particle distribution for each wave function, and this distribution can be interpreted as a special geometric locus in the gravitational dual. Studying the wave functions associated to half-BPS giant gravitons, we are able to show that the matrix model can measure the Planck scale directly. We also show that the output of our simulation seems to match various theoretical expectations in the large N limit and that it captures 1/N effects as statistical fluctuations of the Boltzman gas with the expected scaling. Our results suggest that this is a very promising approach to explore quantum corrections and effects in gravitational physics on AdS spaces.

40 pages, 7 figures, uses JHEP. v2: references added

References in corpus (4)

• Giant Magnons
• A description of 1/4 BPS configurations in minimal type IIB SUGRA
• Aspects of emergent geometry in the AdS/CFT context
• Emergent Classical Strings from Matrix Model

Cited by in corpus (20)

• Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics
• Giant Gravitons - with Strings Attached (III)
• Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity
• Direct test of the gauge-gravity correspondence for Matrix theory correlation functions
• Testing a novel large-N reduction for N=4 super Yang-Mills theory on RxS^3
• Geometry and topology of bubble solutions from gauge theory
• 1/4-BPS M-theory bubbles with SO(3) x SO(4) symmetry
• Direct test of the AdS/CFT correspondence by Monte Carlo studies of N=4 super Yang-Mills theory
• Numerical tests of AdS/CFT at strong coupling
• Giant magnon bound states from strongly coupled N=4 SYM
• Strings on conifolds from strong coupling dynamics, part I
• Strings on conifolds from strong coupling dynamics: quantitative results
• Topology change in commuting saddles of thermal N=4 SYM theory
• Strings on Bubbling Geometries
• A non-perturbative formulation of N=4 super Yang-Mills theory based on the large-N reduction
• Phases of Thermal N=2 Quiver Gauge Theories
• Interior analysis, stretched technique and bubbling geometries
• Eigenvalue Dynamics for Multimatrix Models
• Shaping up BPS States with Matrix Model Saddle Points
• Black Hole Production from High Energy Scattering in AdS/CFT