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On the Spontaneous Breakdown of Lorentz Symmetry in Matrix Models of Superstrings

J. Ambjorn·K. N. Anagnostopoulos·W. Bietenholz·F. Hofheinz·J. Nishimura
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Abstract

In string or M theories, the spontaneous breaking of 10D or 11D Lorentz symmetry is required to describe our space-time. A direct approach to this issue is provided by the IIB matrix model. We study its 4D version, which corresponds to the zero volume limit of 4D super SU(N) Yang-Mills theory. Based on the moment of inertia as a criterion, spontaneous symmetry breaking (SSB) seems to occur, so that only one extended direction remains, as first observed by Bialas, Burda et al. However, using Wilson loops as probes of space-time we do not observe any sign of SSB in Monte Carlo simulations where N is as large as 48. This agrees with an earlier observation that the phase of the fermionic integral, which is absent in the 4D model, should play a crucial role if SSB of Lorentz symmetry really occurs in the 10D IIB matrix model.

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J. Ambjorn, K. N. Anagnostopoulos, W. Bietenholz, F. Hofheinz, J. Nishimura. 2001-05-23. On the Spontaneous Breakdown of Lorentz Symmetry in Matrix Models of Superstrings. https://doi.org/10.1103/physrevd.65.086001

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