Matrix Models, Open Strings and Quantization of Membranes

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We present an approach to membrane quantization using matrix quantum mechanics at large N. We show that this leads (through a simple field theory of two-dimensional open strings and the associated SU(\infty) current algebra) to a 4-D dynamics of self-dual gravity plus matter.
A talk given at the Argonne Duality Institute, June 27-July 12, 1996, 8 pages, Latex. Replaced version contains corrections of minor typos and added references

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