Matrix models, large \(N\) limits and noncommutative solitons

zbMATH Open1111.81145arXivhep-th/0512068MaRDI QIDQ874380

Publication date: 5 April 2007

Published in: Journal of Geometry and Symmetry in Physics (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/hep-th/0512068

Mathematics Subject Classification ID

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

Related Items (11)

More on the new large \(D\) limit of matrix models ⋮ Solving matrix models in the 1/N-expansion ⋮ Phases of the goldstone multitrace matrix model in the large-\(n\)-limit ⋮ \(D\)-dimensional induced gauge theory as a solvable matrix model ⋮ PROJECTORS, MATRIX MODELS AND NONCOMMUTATIVE MONOPOLES ⋮ Large \(N\) structure of the IIB matrix model ⋮ Matrix quantum mechanics and soliton regularization of noncommutative field theory ⋮ Renormalization group approach to matrix models via noncommutative space ⋮ Aspects of noncommutative dynamics: fields ⋮ Power-counting theorem for non-local matrix models and renormalisation ⋮ Cubic constraints for the resolvents of the ABJM matrix model and its cousins

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