Convergence of the Gaussian Expansion Method in Dimensionally Reduced Yang-Mills Integrals

TL;DR

This paper demonstrates the convergence of the Gaussian expansion method in dimensionally reduced Yang-Mills integrals, showing it aligns well with Monte Carlo results, especially for higher dimensions, and is promising for string theory models.

Contribution

The paper systematically proves the convergence of the Gaussian expansion method in a Yang-Mills model, extending its applicability to high-dimensional theories like the IIB matrix model.

Findings

Convergence observed up to 7th order in large-N limit.

Method converges rapidly for D ≥ 10, at 3rd order.

Aligns well with Monte Carlo results.

Abstract

We advocate a method to improve systematically the self-consistent harmonic approximation (or the Gaussian approximation), which has been employed extensively in condensed matter physics and statistical mechanics. We demonstrate the {\em convergence} of the method in a model obtained from dimensional reduction of SU($N$) Yang-Mills theory in $D$ dimensions. Explicit calculations have been carried out up to the 7th order in the large-N limit, and we do observe a clear convergence to Monte Carlo results. For $D \gtrsim 10$ the convergence is already achieved at the 3rd order, which suggests that the method is particularly useful for studying the IIB matrix model, a conjectured nonperturbative definition of type IIB superstring theory.