The shape of emergent quantum geometry from an N=4 SYM minisuperspace approximation

Abstract

We study numerically various wave functions in a gauged matrix quantum mechanics of six commuting hermitian $N\times N$ matrices. Our simulations span ranges of $N$ up to 10000. This system is a truncated and quenched version of N=4 SYM that serves as a minisuperspace approximation to the full $\mathcal{N}=4$ SYM system. This setup encodes aspects of the geometry of the AdS dual in terms of joint eigenvalue distributions for the matrices in the large $N$ limit. We analyze the problem of determining geometric measurements from these fluctuating distributions at finite $N$ and how fast they approach to the large N limit. We treat this eigenvalue geometry information as a proxy for geometric calculations in quantum gravity in a description where gravity is an emergent phenomenon. Our results show that care is needed in choosing the observables that measure the geometry: different choices of observables give different answers, have different size fluctuations at finite $N$ and they converge at different rates to the large $N$ limit. We find that some natural choices of observables are pathological at finite $N$ for $N$ sufficiently small. Finally, we note that the approach to the large $N$ limit does not seem to follow the expected convergence in powers of $1/N^2$ from planar diagram arguments. Our evidence suggests that different powers of $N$ appear, but convergence to large $N$ is rather slow so the values of $N$ we have explored might be too small to conclude this unambiguously.

33 pages, 13 figures

References in corpus (10)

• Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature
• Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics
• The causal set approach to quantum gravity
• Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics
• N=4 Super Yang-Mills from the Plane Wave Matrix Model
• Multi-matrix models and emergent geometry
• Testing a novel large-N reduction for N=4 super Yang-Mills theory on RxS^3
• Aspects of emergent geometry in the AdS/CFT context
• Geometry and topology of bubble solutions from gauge theory
• Numerical tests of AdS/CFT at strong coupling