Matrix Theory on ALE Spaces and Wrapped Membranes

Details Matrix Theory on ALE Spaces and Wrapped Membranes Matrix Theory on ALE Spaces and Wrapped Membranes

1998-03-05

arxiv.org/abs/hep-th/9803048v1

Nucl.Phys. B529 (1998) 225-245

Physics

High Energy Physics

High Energy Physics - Theory

23 pages LaTeX2e, 1 figure, using utarticle.cls (included), array.sty, amsmath.sty, amsfonts.sty, cite.sty, epsfig. Bibtex sty

Scientific paper

10.1016/S0550-3213(98)00347-2

We study the properties of wrapped membranes in matrix theory on ALE spaces. We show that the only BPS bound states of wrapped membranes that can form are roots of the $A$-$D$-$E$ group. We determine a bound on the energy of a bound state and find the correct dependence on the blow-up parameters and longitudinal momentum expected from M-Theory. For the $A_{n-1}$ series, we construct explicit classical solutions for the wrapped membrane bound states. These states have a very rich structure and have a natural interpretation in terms of noncommutative geometry. In the $A_1$ case, we examine the spectrum of excitations around the wrapped membrane solution and provide an explicit calculation of their energies. The results agree exactly with supergravity calculations.

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