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 hyperbolic sigma-models are investigated. The existence of a large asymptotic expansion is proven on finite lattices of dimension . 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.
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