Topological Symmetry, Background Independence, and Matrix Models

Details Topological Symmetry, Background Independence, and Matrix Models Topological Symmetry, Background Independence, and Matrix Models

1998-06-12

arxiv.org/abs/hep-th/9806096v1

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, LaTex, Invited paper to appear in the special issue of the Journal of Chaos, Solitons and Fractals on "Superstrings,

Scientific paper

We illustrate a physical situation in which topological symmetry, its breakdown, space-time uncertainty principle, and background independence may play an important role in constructing and understanding matrix models. First, we show that the space-time uncertainty principle of string may be understood as a manifestation of the breakdown of the topological symmetry in the large $N$ matrix model. Next, we construct a new type of matrix models which is a matrix model analog of the topological Chern-Simons and BF theories. It is of interest that these topological matrix models are not only completely independent of the background metric but also have nontrivial "p-brane" solutions as well as commuting classical space-time as the classical solutions. In this paper, we would like to point out some elementary and unsolved problems associated to the matrix models, whose resolution would lead to the more satisfying matrix model in future.

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