On the large N expansion in hyperbolic sigma-models

Details On the large N expansion in hyperbolic sigma-models On the large N expansion in hyperbolic sigma-models

2007-11-23

arxiv.org/abs/0711.3756v2

J.Math.Phys.49:073301,2008

Physics

Mathematical Physics

15 pages. Some changes in introduction and discussion; to appear in J. Math. Phys

Scientific paper

10.1063/1.2951886

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.

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