Fuzzy Nambu-Goldstone physics

Dec, 2002
18 pages
Published in:
  • Int.J.Mod.Phys.A 18 (2003) 5931-5948
e-Print:
Report number:
  • SU-4252-763,
  • DFUP-02-13

Citations per year

200320062009201220153401
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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