Improved Perturbation Method and its Application to the IIB Matrix Model

Abstract

We present a new scheme for extracting approximate values in ``the improved perturbation method'', which is a sort of resummation technique capable of evaluating a series outside the radius of convergence. We employ the distribution profile of the series that is weighted by nth-order derivatives with respect to the artificially introduced parameters. By those weightings the distribution becomes more sensitive to the ``plateau'' structure in which the consistency condition of the method is satisfied. The scheme works effectively even in such cases that the system involves many parameters. We also propose that this scheme has to be applied to each observables separately and be analyzed comprehensively. We apply this scheme to the analysis of the IIB matrix model by the improved perturbation method obtained up to eighth order of perturbation in the former works. We consider here the possibility of spontaneous breakdown of Lorentz symmetry, and evaluate the free energy and the anisotropy of space-time extent. In the present analysis, we find an SO(10)-symmetric vacuum besides the SO(4)- and SO(7)-symmetric vacua that have been observed. It is also found that there are two distinct SO(4)-symmetric vacua that have almost the same value of free energy but the extent of space-time is different. From the approximate values of free energy, we conclude that the SO(4)-symmetric vacua are most preferred among those three types of vacua.

52 pages, published version

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Cited by in corpus (13)

• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings
• Exact fuzzy sphere thermodynamics in matrix quantum mechanics
• Boundary condition for D-brane from Wilson loop, and gravitational interpretation of eigenvalue in matrix model in AdS/CFT correspondence
• 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
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models
• Spontaneous Supersymmetry Breaking by Large-N Matrices
• A Renormalization Group Approach to A Yang-Mills Two Matrix Model
• Improved Taylor Expansion method in the Ising model
• Dynamical Generation of Non-Abelian Gauge Group via the Improved Perturbation Theory
• Dynamical Compactification of Extra Dimensions in the Euclidean IKKT Matrix Model via Spontaneous Symmetry Breaking