Noncommutative Gauge Theories on Fuzzy Sphere and Fuzzy Torus from Matrix Model | Zendy

Yusuke Kimura | Zendy

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Noncommutative Gauge Theories on Fuzzy Sphere and Fuzzy Torus from Matrix Model

Author(s) -

Yusuke Kimura

Publication year - 2001

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.106.445

Subject(s) - noncommutative geometry , fuzzy sphere , physics , gauge theory , torus , mathematical physics , embedding , limit (mathematics) , commutative property , matrix (chemical analysis) , pure mathematics , mathematics , mathematical analysis , geometry , materials science , composite material , artificial intelligence , computer science

We consider a reduced model of four-dimensional Yang-Mills theory with a massterm. This matrix model has two classical solutions, two-dimensional fuzzysphere and two-dimensional fuzzy torus. These classical solutions areconstructed by embedding them into three or four dimensional flat space. Theyexist for finite size matrices, that is, the number of the quantum on thesemanifolds is finite. Noncommutative gauge theories on these noncommutativemanifolds are derived by expanding the model around these classical solutionsand studied by taking two large $N$ limits, a commutative limit and a largeradius limit. The behaviors of gauge invariant operators are also discussed.Comment: 30 Pages, references added and some comments correcte

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