Simplicial Chiral Models

TL;DR

This paper introduces and analytically studies simplicial chiral models on a d-1 dimensional simplex, solving specific cases and exploring their connections to lattice models and matrix systems in the large N limit.

Contribution

It provides explicit solutions for simplicial chiral models at dimensions 0, 2, 4, and infinity, and discusses their relation to lattice models and matrix systems.

Findings

Explicit solutions for models at d=0, 2, 4, and infinity.

Established relationships with standard lattice models.

Connected the models to few-matrix systems in the double scaling limit.

Abstract

Principal chiral models on a d-1 dimensional simplex are introduced and studied analytically in the large $N$ limit. The $d = 0, 2, 4$ and $\infty$ models are explicitly solved. Relationship with standard lattice models and with few-matrix systems in the double scaling limit are discussed.