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 H2, 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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Communicated by M. Aizenman
Dedicated to Freeman Dyson on the Occasion of his eightieth birthday
Acknowledgement T. Spencer would like to thank M. Disertori, K. Gawedzki, G. Papanicolau and S.R.S. Varadhan for helpful comments.
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Spencer, T., Zirnbauer, M. Spontaneous Symmetry Breaking of a Hyperbolic Sigma Model in Three Dimensions. Commun. Math. Phys. 252, 167–187 (2004). https://doi.org/10.1007/s00220-004-1223-3
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DOI: https://doi.org/10.1007/s00220-004-1223-3