Topological Symmetry, Background Independence, and Matrix Models

Abstract

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.

19 pages, LaTex, Invited paper to appear in the special issue of the Journal of Chaos, Solitons and Fractals on "Superstrings, M, F, S, ....... Theory", edited by M.S. El Naschie and C. Castro

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• A Large-N Reduced Model as Superstring
• D-Particle Dynamics and The Space-Time Uncertainty Relation
• Schild Action and Space-Time Uncertainty Principle in String Theory
• Path Integral Equivalence between Super D-string and IIB Superstring
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Cited by in corpus (2)

• Nambu-Goto Strings from SU(N) Born-Infeld model
• The Search for the Origins of M Theory : Loop Quantum Mechanics, Loops/Strings and Bulk/Boundary Dualities