Improved Perturbation Method and its Application to the IIB Matrix Model

TL;DR

This paper introduces an improved perturbation method that enhances the evaluation of series outside their convergence radius, and applies it to analyze the IIB matrix model, revealing multiple vacua and favoring SO(4) symmetry.

Contribution

The paper develops a new scheme for the improved perturbation method, enabling more accurate analysis of complex systems like the IIB matrix model.

Findings

Discovery of an SO(10)-symmetric vacuum.

Identification of two distinct SO(4)-symmetric vacua.

SO(4)-symmetric vacua are most energetically favorable.

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.