Bootstraps to strings: solving random matrix models with positivite

Abstract

A new approach to solving random matrix models directly in the large N limit is developed. First, a set of numerical values for some low-pt correlation functions is guessed. The large N loop equations are then used to generate values of higher-pt correlation functions based on this guess. Then one tests whether these higher-pt functions are consistent with positivity requirements, e.g., (tr M2k) ≥ 0. If not, the guessed values are systematically ruled out. In this way, one can constrain the correlation functions of random matrices to a tiny subregion which contains (and perhaps converges to) the true solution. This approach is tested on single and multi-matrix models and handily reproduces known solutions. It also produces strong results for multi-matrix models which are not believed to be solvable. A tantalizing possibility is that this method could be used to search for new critical points, or string worldsheet theories.

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Lin, H.W. Bootstraps to strings: solving random matrix models with positivite. J. High Energ. Phys. 2020, 90 (2020). https://doi.org/10.1007/JHEP06(2020)090

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Keywords

  • Matrix Models
  • 1/N Expansion
  • Field Theories in Lower Dimensions