Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-06-08
Int.J.Mod.Phys. A14 (1999) 4395-4456
Physics
High Energy Physics
High Energy Physics - Theory
77 pages, 21 eps figures, 1 table, LaTeX2.09; an invited review article
Scientific paper
10.1142/S0217751X99002074
This is a review article in which we will introduce, in a unifying fashion and with more intermediate steps in some difficult calculations, two infinite-dimensional Lie algebras of quantum matrix models, one for the open string sector and one for the closed string sector. Physical observables of quantum matrix models in the large-N limit can be expressed as elements of these Lie algebras. We will see that both algebras arise as quotient algebras of a larger Lie algebra. We will also discuss some properties of these Lie algebras not published elsewhere yet, and briefly review their relationship with well-known algebras like the Cuntz algebra, the Witt algebra and the Virasoro algebra. We will also review how Yang--Mills theory, various low energy effective models of string theory, quantum gravity, string-bit models, and quantum spin chain models can be formulated as quantum matrix models. Studying these algebras thus help us understand the common symmetry of these physical systems.
Lee C.-W. H.
Rajeev Sarada. G.
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