Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-12-11
Int.J.Mod.Phys. A18 (2003) 5931-5948
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 18 pages; references added, typos corrected
Scientific paper
10.1142/S0217751X03017440
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.
Balachandran Aiyalam P.
Immirzi Giorgio
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