TL;DR
This paper investigates spiky membrane configurations within SO(d)xSU(N) matrix models, presenting exact solutions and analyzing their behavior in the large N limit, revealing a connection to harmonic oscillator ground states.
Contribution
It introduces a class of exact solutions for membrane configurations in matrix models and explores their properties as N approaches infinity.
Findings
Large N wavefunctions resemble harmonic oscillator ground states.
Exact solutions analogous to plane-waves are identified.
Membrane configurations exhibit specific scaling behaviors.
Abstract
We study spiky configurations of membranes in the SO(d)xSU(N) invariant matrix models. A class of exact solutions (analogous to plane-waves) of the corresponding Schroedinger equation for an arbitrary N is discussed. If the large N limit is performed so that the energy scales like N^2, the N=infinity wavefunctions reduce to the ground state of the d-dimensional harmonic oscillator.
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