Spontaneous symmetry breaking of a hyperbolic sigma model in three dimensions

Abstract

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.

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

References in corpus (2)

• Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation
• Density of states for Random Band Matrix

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