Comments on the Large N Matrix Model.

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  • Kajiura Hiroshige
    Graduate School of Mathematical Sciences, University of Tokyo, Tokyo 153–8914, Japan
  • Kato Akishi
    Graduate School of Mathematical Sciences, University of Tokyo, Tokyo 153–8914, Japan
  • Ogushi Sachiko
    Department of Physics, Ochanomizu University, Tokyo 112–8610, Japan

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In the matrix model approach to M/string theory, a general prescription of the large N limit is still elusive. To gain insights into the scaling limit, we study the quantum fluctuations around a given diagonal background of the large N matrix model in the weakly coupled regime. The perturbative expansion in matrix theory is explicitly shown to be identical to the Feynman amplitudes of gauge theory, provided that the D instanton configuration space is interpreted as (discretized) loop momentum space. This enables us to study how the structure of large N divergence is related to the ordinary UV/IR divergences in QFT. Various bounds on the scaling exponents are also discussed.

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