Instantons and Chiral Anomaly in Fuzzy Physics
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This paper develops discrete quantum field theories on fuzzy manifolds using noncommutative geometry and presents discrete representations of θ-terms and topological susceptibility for gauge theories and derives axial anomaly on the fuzzy sphere.Abstract:
In continuum physics, there are important topological aspects like instantons, theta-terms and the axial anomaly. Conventional lattice discretizations often have difficulties in treating one or the other of these aspects. In this paper, we develop discrete quantum field theories on fuzzy manifolds using noncommutative geometry. Basing ourselves on previous treatments of instantons and chiral fermions (without fermion doubling) on fuzzy spaces and especially fuzzy spheres, we present discrete representations of theta-terms and topological susceptibility for gauge theories and derive axial anomaly on the fuzzy sphere. Our gauge field action for four dimensions is bounded by the modulus of the instanton number as in the continuum.read more
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Noncommutative gauge theory on fuzzy sphere from matrix model
Satoshi Iso,Satoshi Iso,Yusuke Kimura,Yusuke Kimura,Kanji Tanaka,Kanji Tanaka,Kazunori Wakatsuki,Kazunori Wakatsuki +7 more
TL;DR: A noncommutative U(1) and U(n) gauge theory on the fuzzy sphere is derived from a three-dimensional matrix model by expanding the model around a classical solution of the fuzzy spheres.
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Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model
TL;DR: The partition function of U(n) Yang-Mills theory on the classical sphere is recovered in the large N limit, as a sum over instanton contributions.
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Lectures on Fuzzy and Fuzzy Susy Physics
TL;DR: Fuzzy Spaces Star Products Scalar Fields on the Fuzzy Sphere Instantons, Monopoles and Projective Modules as discussed by the authors The Dirac Operator and Axial Anomaly.
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Fuzzy CP**2
TL;DR: This paper reports on the work on the “fuzzification” of the four-dimensional CP 2 and its QFT’s, which is not spin, but spinc, and has many unique features.
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Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
TL;DR: In this article, a renormalizable 4-dimensional SU(N) gauge theory with a suitable multiplet of scalar fields is presented, which dynamically develops extra dimensions in the form of a fuzzy sphere S 2 N.
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TL;DR: In this paper, a comprehensive and coherent account of the theory of quantum fields on a lattice, an essential technique for the study of the strong and electroweak nuclear interactions, is presented.
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Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
TL;DR: In this paper, it was shown that the Ginsparg-Wilson relation implies an exact symmetry of the fermion action, which may be regarded as a lattice form of an infinitesimal chiral rotation.
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An Introduction to Noncommutative Spaces and Their Geometries
TL;DR: The Spectral Calculus as mentioned in this paper is a generalization of K-theory for non-commutative spaces and algebraic spaces and algebras of functions, and it is used in Projective Systems of Non-Commutative Lattices.
Posted Content
An Introduction to Noncommutative Spaces and their Geometry
TL;DR: In this paper, the authors present an introduction to recent work on non-commutative lattices, which have been used to construct topologically nontrivial quantum mechanical and field theory models, in particular alternative models of lattice gauge theory.