Mean Field Approximation of IIB Matrix Model and Emergence of Four Dimensional Space-Time

Abstract

For the purpose of analyzing non-perturbative dynamics of string theory, Nishimura and Sugino have applied an improved mean field approximation (IMFA) to IIB matrix model. We have extracted the essence of the IMFA and obtained a general scheme, an improved Taylor expansion, that can be applied to a wide class of series which is not necessarily convergent. This approximation scheme with the help of the 2PI free energy enables us to perform higher order calculations. We have shown that the value of the free energy is stable at higher orders, which supports the validity of the approximation. Moreover, the ratio between the extent of ``our'' space-time and that of the internal space is found to increase rapidly as we take the higher orders into account. Our results suggest that the four dimensional space-time emerges spontaneously in IIB matrix model.

43 pages, 108 eps files and 1 style file included, some typos, symmetry factors, and graphs are corrected. final version

References in corpus (17)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Large N Field Theories, String Theory and Gravity
• Dirichlet-Branes and Ramond-Ramond Charges
• M Theory As A Matrix Model: A Conjecture
• A Large-N Reduced Model as Superstring
• IIB Matrix Model
• Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model
• Monte Carlo Studies of the IIB Matrix Model at Large N
• Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model
• Brane world from IIB matrices
• Approximations for strongly-coupled supersymmetric quantum mechanics
• M theory as a matrix extension of Chern-Simons theory
• Supermatrix Models
• Exactly Solvable Matrix Models for the Dynamical Generation of Space-Time in Superstring Theory
• Gaussian and Mean Field Approximations for Reduced Yang-Mills Integrals
• The exceptional Jordan algebra and the matrix string
• Gaussian and Mean Field Approximations for Reduced 4D Supersymmetric Yang-Mills Integral

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