The Algebras of Large N Matrix Mechanics

M. B. Halpern; C. Schwartz

doi:10.1142/s0217751x99001482

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arXiv · hep-th/9809197

The Algebras of Large N Matrix Mechanics

M. B. Halpern·C. Schwartz

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Abstract

Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.

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M. B. Halpern, C. Schwartz. 1999-09-16. The Algebras of Large N Matrix Mechanics. https://doi.org/10.1142/s0217751x99001482

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