Higher Order Terms in the Improved Mean Field Approximation for the IIB Matrix Model and the Emergence of Four-Dimensional Space-Time | Zendy

Tatsumi Aoyama | Zendy; H. Kawai | Zendy

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Higher Order Terms in the Improved Mean Field Approximation for the IIB Matrix Model and the Emergence of Four-Dimensional Space-Time

Author(s) -

Tatsumi Aoyama,

H. Kawai

Publication year - 2006

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.116.405

Subject(s) - ansatz , physics , space (punctuation) , matrix (chemical analysis) , mathematical physics , symmetry (geometry) , plateau (mathematics) , matrix model , field (mathematics) , series (stratigraphy) , order (exchange) , planar , mathematical analysis , pure mathematics , mathematics , geometry , paleontology , philosophy , linguistics , materials science , computer graphics (images) , finance , composite material , computer science , economics , string (physics) , biology

The spontaneous breakdown of SO(10) symmetry of the IIB matrix model has beenstudied by using the improved mean field approximation (IMFA). In this report,the eighth-order contribution to the improved perturbative series is obtained,which involves evaluation of 20410 planar two-particle irreducible vacuumdiagrams. We consider SO(d)-preserving configurations as ansatz (d=4,7). Thedevelopment of plateau, the solution of self-consistency condition, is seen inboth ansatz. The large ratio of the space-time extent of d-dimensional partagainst the remaining (10-d)-dimensional part is obtained for SO(4) ansatzevaluated at the representative points of the plateau. It would be interpretedas the emergence of four-dimensional space-time in the IIB matrix model.Comment: 13 page

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