English

On the large N expansion in hyperbolic sigma-models

Mathematical Physics 2008-11-26 v2 High Energy Physics - Lattice High Energy Physics - Theory math.MP

Abstract

Invariant correlation functions for SO(1,N){\rm SO}(1,N) hyperbolic sigma-models are investigated. The existence of a large NN asymptotic expansion is proven on finite lattices of dimension d2d \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.

Keywords

Cite

@article{arxiv.0711.3756,
  title  = {On the large N expansion in hyperbolic sigma-models},
  author = {Max Niedermaier and Erhard Seiler},
  journal= {arXiv preprint arXiv:0711.3756},
  year   = {2008}
}

Comments

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

R2 v1 2026-06-21T09:46:42.182Z