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

Jun Nishimura·Toshiyuki Okubo·Fumihiko Sugino
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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.

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Jun Nishimura, Toshiyuki Okubo, Fumihiko Sugino. 2002-11-06. Convergence of the Gaussian Expansion Method in Dimensionally Reduced Yang-Mills Integrals. https://doi.org/10.1088/1126-6708%2F2002%2F10%2F043

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