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

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

2002-05-24

arxiv.org/abs/hep-th/0205253v2

JHEP 0210 (2002) 043

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 4 pages, 5 figures; title slightly changed, explanations added (16 pages, 14 figures), final version published in JHEP

Scientific paper

10.1088/1126-6708/2002/10/043

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.

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