Spontaneous symmetry breaking of a hyperbolic sigma model in three dimensions

Details Spontaneous symmetry breaking of a hyperbolic sigma model in three dimensions Spontaneous symmetry breaking of a hyperbolic sigma model in three dimensions

2004-10-11

arxiv.org/abs/math-ph/0410032v1

Commun.Math.Phys. 252 (2004) 167-187

Physics

Mathematical Physics

21 pages, dedicated to F.J. Dyson on the occasion of his 80th birthday

Scientific paper

10.1007/s00220-004-1223-3

Non-linear sigma models that arise from the supersymmetric approach to disordered electron systems contain a non-compact bosonic sector. We study the model with target space H^2, the two-hyperboloid with isometry group SU(1,1), and prove that in three dimensions moments of the fields are finite in the thermodynamic limit. Thus the non-compact symmetry SU(1,1) is spontaneously broken. The bound on moments is compatible with the presence of extended states.

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