On the large N expansion in hyperbolic sigma-models

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Invariant correlation functions for ${\rm SO}(1,N)$ hyperbolic sigma-models are investigated. The existence of a large $N$ asymptotic expansion is proven on finite lattices of dimension $d \geq 2$. The unique saddle point configuration is characterized by a negative gap vanishing at least like 1/V with the volume. Technical difficulties compared to the compact case are bypassed using horospherical coordinates and the matrix-tree theorem.
15 pages. Some changes in introduction and discussion; to appear in J. Math. Phys

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Mathematical Physics, High Energy Physics - Lattice, High Energy Physics - Theory, 41A60; 82B80

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http://salesiana.dossiersoluciones.com/handle/123456789/204871

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0711.3756
 http://arxiv.org/abs/0711.3756
 J.Math.Phys.49:073301,2008
 doi:10.1063/1.2951886

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arXiv