On the large N expansion in hyperbolic sigma-models

Abstract

Invariant correlation functions for $\mathrm{SO}(1,N)$ hyperbolic sigma-models are investigated. The existence of a large $N$ asymptotic expansion is proven on finite lattices of dimension $d\ge 2$. 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

References in corpus (4)

• Spontaneous symmetry breaking of a hyperbolic sigma model in three dimensions
• Vacuum orbit and spontaneous symmetry breaking in hyperbolic sigma models
• Perturbative and nonperturbative correspondences between compact and non-compact sigma-models
• Noncompact sigma-models: Large N expansion and thermodynamic limit

Cited by in corpus (3)

• Noncompact sigma-models: Large N expansion and thermodynamic limit
• The curious case of large-N expansions on a (pseudo)sphere
• Non-linear sigma models on constant curvature target manifolds: a functional renormalization group approach