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Matrix models, large \(N\) limits and noncommutative solitons. (English) Zbl 1111.81145

Summary: A survey of the interrelationships between matrix models and field theories on the noncommutative torus is presented. The discretization of noncommutative gauge theory by twisted reduced models is described along with a rigorous definition of the large \(N\) continuum limit. The regularization of arbitrary noncommutative field theories by means of matrix quantum mechanics and its connection to noncommutative solitons is also discussed.

MSC:

81T75 Noncommutative geometry methods in quantum field theory
58B32 Geometry of quantum groups
35Q51 Soliton equations
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
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