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Gaussian expansion analysis of a matrix model with the spontaneous breakdown of rotational symmetry

Jun Nishimura·Toshiyuki Okubo·Fumihiko Sugino
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Abstract

Recently the gaussian expansion method has been applied to investigate the dynamical generation of 4d space-time in the IIB matrix model, which is a conjectured nonperturbative definition of type IIB superstring theory in 10 dimensions. Evidence for such a phenomenon, which is associated with the spontaneous breaking of the SO(10) symmetry down to SO(4), has been obtained up to the 7-th order calculations. Here we apply the same method to a simplified model, which is expected to exhibit an analogous spontaneous symmetry breaking via the same mechanism as conjectured for the IIB matrix model. The results up to the 9-th order demonstrate a clear convergence, which allows us to unambiguously identify the actual symmetry breaking pattern by comparing the free energy of possible vacua and to calculate the extent of ``space-time'' in each direction.

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Jun Nishimura, Toshiyuki Okubo, Fumihiko Sugino. 2004-12-17. Gaussian expansion analysis of a matrix model with the spontaneous breakdown of rotational symmetry. https://doi.org/10.1143/ptp.114.487

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