Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model

We study the spontaneous breakdown of SO(10) symmetry in the IIB matrixmodel, a conjectured nonperturbative definition of type IIB superstring theoryin ten dimensions. Our analysis is based on a Gaussian expansion technique,which was originally proposed by Kabat-Lifschytz and applied successfully tothe strong coupling dynamics of the Matrix Theory. We propose a prescriptionfor including higher order corrections, which yields a rapid convergence in asimple example. This prescription is then applied to the IIB matrix model up tothe third order. We find that the `self-consistency equations' allow varioussymmetry breaking solutions. Among them, the solution preserving SO(4) symmetryis found to have the smallest free energy. The value of the free energy comescloser to the analytic formula obtained by Krauth-Nicolai-Staudacher as weincrease the order. The extent of the space-time in the 4 directions is largerthan the remaining 6 directions, and the ratio increases with the order. Theseresults provide the first analytical evidence that four-dimensional space-timeis generated dynamically in the IIB matrix model.Comment: 10 pages, no figure, LaTeX; corrected errors about ansat