出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：The IIB matrix model proposes a mechanism for dynamically generating four dimensional space– time in string theory by spontaneous breaking of the ten dimensional rotational symmetry SO(10). Calculations using the Gaussian expansion method (GEM) lend support to this conjecture. We study a simple SO(4) invariant matrix model using Monte Carlo simulations and we confirm that its rotational symmetry breaks down, showing that lower dimensional configurations dominate the path integral. The model has a strong complex action problem and the calculations were made possible by the use of the factorization method on the density of states rn(x) of properly nor- malized eigenvalues ˜l n of the space–time moment of inertia tensor. We study scaling properties of the factorized terms of rn(x) and we find them in agreement with simple scaling arguments. These can be used in the finite size scaling extrapolation and in the study of the region of con- figuration space obscured by the large fluctuations of the phase. The computed values of ˜l n are in reasonable agreement with GEM calculations and a numerical method for comparing the free energy of the corresponding ansatze is proposed and tested.
