Twisted Eguchi-Kawai Reduced Chiral Models

TL;DR

This paper investigates the validity of the twisted Eguchi-Kawai reduction for large-N principal chiral models using Monte Carlo simulations, confirming its effectiveness in the strong-coupling region but not in the weak-coupling regime.

Contribution

It provides numerical evidence on the applicability of TEK reduction to two-dimensional principal chiral models across different coupling regimes.

Findings

TEK reduction is consistent in the strong-coupling region.

TEK reduction does not hold in the weak-coupling (continuum) limit.

Implications for noncommutative field theories are discussed.

Abstract

We study the twisted Eguchi-Kawai (TEK) reduction procedure for large-N unitary matrix lattice models. In particular, we consider the case of two-dimensional principal chiral models, and use numerical Monte Carlo (MC) simulations to check the conjectured equivalence of TEK reduced model and standard lattice model in the large-N limit. The MC results are compared with the large-N limit of lattice principal chiral models to verify the supposed equivalence. The consistency of the TEK reduction procedure is verified in the strong-coupling region, i.e. for $\beta<\beta_c$ where $\beta_c$ is the location of the large-N phase transition. On the other hand, in the weak-coupling regime $\beta>\beta_c$, relevant for the continuum limit, our MC results do not support the equivalence of the large-N limits of the lattice chiral model and the corresponding TEK reduction. The implications for the correspondence between TEK model and noncommutative field theory are also discussed.