Non-commutative principal chiral models

TL;DR

This paper explores the equivalence between twisted Eguchi-Kawai reduced chiral models and non-commutative U(1) theories, proposing a double scaling limit and supporting it with numerical evidence.

Contribution

It introduces a novel connection between reduced chiral models and non-commutative theories, and proposes a new numerical approach to study the continuum limit.

Findings

Numerical results support the proposed double scaling limit.

The reduced models are consistent with the non-commutative parent theory.

The approach offers a new way to investigate non-commutative vacuum dynamics.

Abstract

Twisted Eguchi-Kawai reduced chiral models are shown to be formally equivalent to a U(1) non-commutative parent theory. The non-commutative theory describes the vacuum dynamics of the non-commutative charged tachyonic field of a brane system. To make contact with the continuum non-commutative theory, a double scaling large N limit for the reduced model is required. We show a possible limiting procedure, which we propose to investigate numerically. Our numerical results show substantial consistency with the outlined procedure