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

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.

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

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Cited by in corpus (17)

• 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
• Dijkgraaf-Vafa theory as large-N reduction
• High temperature expansion in supersymmetric matrix quantum mechanics
• Dynamical generation of gauge groups in the massive Yang-Mills-Chern-Simons matrix model
• Perturbative versus nonperturbative dynamics of the fuzzy S^2*S^2
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping
• Spontaneous supersymmetry breaking in large-$N$ matrix models with slowly varying potential
• Matrix geometries and Matrix Models
• Improved Perturbation Method and its Application to the IIB Matrix Model
• Testing the Gaussian expansion method in exactly solvable matrix models
• Nuclear states and spectra in holographic QCD
• Adding a Myers Term to the IIB Matrix Model
• Dynamical Generation of Non-Abelian Gauge Group via the Improved Perturbation Theory
• Lattice Superstring and Noncommutative Geometry
• Partition Functions of Reduced Matrix Models with Classical Gauge Groups