On Stable Sector in Supermembrane Matrix Model

Abstract

We study the spectrum of SU(2) x SO(2) matrix supersymmetric quantum mechanics. We use angular coordinates that allow us to find an explicit solution of the Gauss law constraints and single out the quantum number n (the Lorentz angular momentum). Energy levels are four-fold degenerate with respect to n and are labeled by n_q, the largest n in a quartet. The Schrödinger equation is reduced to two different systems of two-dimensional partial differential equations. The choice of a system is governed by n_q. We present the asymptotic solutions for the systems deriving thereby the asymptotic formula for the spectrum. Odd n_q are forbidden, for even n_q the spectrum has a continuous part as well as a discrete one, meanwhile for half-integer n_q the spectrum is purely discrete. Taking half-integer n_q one can cure the model from instability caused by the presence of continuous spectrum.

29 pages, 5 figures

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Cited by in corpus (8)

• Large N behavior of two dimensional supersymmetric Yang-Mills quantum mechanics
• Maximally Chaotic Dynamical Systems and Fundamental Interactions
• Light-cone SU(2) Yang-Mills theory and conformal mechanics
• Stretched quantum membranes
• Maximally chaotic dynamical systems of Anosov-Kolmogorov
• Optimized Fock space in the large N limit of quartic interactions in Matrix Models
• Supersymmetry and Integrability in Planar Mechanical Systems
• Yang-Mills Classical and Quantum Mechanics and Maximally Chaotic Dynamical Systems