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Testing the Gaussian expansion method in exactly solvable matrix models

Jun Nishimura·Toshiyuki Okubo·Fumihiko Sugino
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Abstract

The Gaussian expansion has been developed since early 80s as a powerful analytical method, which enables nonperturbative studies of various systems using `perturbative' calculations. Recently the method has been used to suggest that 4d space-time is generated dynamically in a matrix model formulation of superstring theory. Here we clarify the nature of the method by applying it to exactly solvable one-matrix models with various kinds of potential including the ones unbounded from below and of the double-well type. We also formulate a prescription to include a linear term in the Gaussian action in a way consistent with the loop expansion, and test it in some concrete examples. We discuss a case where we obtain two distinct plateaus in the parameter space of the Gaussian action, corresponding to different large-N solutions. This clarifies the situation encountered in the dynamical determination of the space-time dimensionality in the previous works.

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Jun Nishimura, Toshiyuki Okubo, Fumihiko Sugino. 2003-10-08. Testing the Gaussian expansion method in exactly solvable matrix models. https://doi.org/10.1088/1126-6708%2F2003%2F10%2F057

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