Fuzzy NambuGoldstone 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 NambuGoldstone modes described by fields with values in G/H. In twodimensional 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 twosphere and describe their fuzzy analogs for G = SU(N+1), H = S(U(N1) ⊗ U(1)) ≃ U(N) and G/H={ C}P^{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) × (N+1) projectors of rank ≤ (N+1)/2. These fuzzy models are finitedimensional matrix models which nevertheless retain all the essential continuum topological features like solitonic sectors. They seem well suited for numerical work.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 2003
 DOI:
 10.1142/S0217751X03017440
 arXiv:
 arXiv:hepth/0212133
 Bibcode:
 2003IJMPA..18.5931B
 Keywords:

 Sigma models;
 noncommutative geometry;
 monopoles;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 Latex, 18 pages