Fuzzy Nambu-Goldstone Physics

Abstract

In spacetime dimensions larger than 2, whenever a global symmetry G is spontaneously broken to a subgroup H, and G and H are Lie groups, there are Nambu-Goldstone modes described by fields with values in G/H. In two-dimensional spacetimes as well, models where fields take values in G/H are of considerable interest even though in that case there is no spontaneous breaking of continuous symmetries. We consider such models when the world sheet is a two-sphere and describe their fuzzy analogues for G=SU(N+1), H=S(U(N-1)xU(1)) ~ U(N) and G/H=CP^N. More generally our methods give fuzzy versions of continuum models on S^2 when the target spaces are Grassmannians and flag manifolds described by (N+1)x(N+1) projectors of rank =< (N+1)/2. These fuzzy models are finite-dimensional matrix models which nevertheless retain all the essential continuum topological features like solitonic sectors. They seem well-suited for numerical work.

Latex, 18 pages; references added, typos corrected

References in corpus (4)

• Monopoles and Solitons in Fuzzy Physics
• Topologically nontrivial field configurations in noncommutative geometry
• Some Properties of Non-linear $\sigma$-Models in Noncommutative Geometry
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• The One-Plaquette Model Limit of NC Gauge Theory in 2D
• Emergent fuzzy geometry and fuzzy physics in $4$ dimensions
• Duality in Fuzzy Sigma Models
• U(2) projectors and 't Hooft-Polyakov monopoles on a fuzzy sphere
• Standard and Non-Standard Quantum Models : A Non-Commutative Version of the Classical System of SU(2) and SU(1,1) Arising from Quantum Optics