Testing the Gaussian expansion method in exactly solvable matrix models

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.

arXiv comment30 pages, 15 figures, LaTeX; added references for section 1

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Cited by in corpus (10)

• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings
• Toward tensor renormalization group study of three-dimensional non-Abelian gauge theory
• Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Spontaneous supersymmetry breaking in large-$N$ matrix models with slowly varying potential
• Improved Perturbation Method and its Application to the IIB Matrix Model
• New critical behavior in a supersymmetric double-well matrix model
• Dynamical Generation of Non-Abelian Gauge Group via the Improved Perturbation Theory
• Fermionic Matrix Models and Bosonization