Dynamical Aspects of Large N Reduced Models

TL;DR

This paper investigates the dynamical properties of large N reduced models of Yang-Mills theory, revealing how space-time coordinates behave and how symmetry breaking occurs or is prevented, through simulations and analytical methods.

Contribution

It provides new insights into the eigenvalue dynamics, space-time extent, and symmetry properties of large N reduced models using Monte Carlo simulations and a 1/D expansion.

Findings

The space-time extent is maximally broken, indicating a highly uncertain space-time coordinate system.

No spontaneous symmetry breaking of Lorentz invariance is observed.

Analytical calculations via 1/D expansion agree with Monte Carlo results.

Abstract

We study the large N reduced model of D-dimensional Yang-Mills theory with special attention to dynamical aspects related to the eigenvalues of the N by N matrices, which correspond to the space-time coordinates in the IIB matrix model. We first put an upper bound on the extent of space time by perturbative arguments. We perform a Monte Carlo simulation and show that the upper bound is actually saturated. The relation of our result to the SSB of the U(1)^D symmetry in the Eguchi-Kawai model is clarified. We define a quantity which represents the uncertainty of the space-time coordinates and show that it is of the same order as the extent of space time, which means that a classical space-time picture is maximally broken. We develop a 1/D expansion, which enables us to calculate correlation functions of the model analytically. The absence of an SSB of the Lorentz invariance is shown by the Monte Carlo simulation as well as by the 1/D expansion.