Fuzzy Nambu-Goldstone physics
Dec, 200218 pages
Published in:
- Int.J.Mod.Phys.A 18 (2003) 5931-5948
e-Print:
- hep-th/0212133 [hep-th]
Report number:
- SU-4252-763,
- DFUP-02-13
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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.- space-time
- dimension: >=2
- field theoretical model: CP(1)
- field theoretical model: CP(N-1)
- sigma model: nonlinear
- fuzzy
- coset space
- space: Grassmann
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