Conformal Field Theory Techniques in Random Matrix models

Details Conformal Field Theory Techniques in Random Matrix models Conformal Field Theory Techniques in Random Matrix models

1999-07-08

arxiv.org/abs/hep-th/9907060v1

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, Based on the talk of the author at the Third Claude Itzykson Meeting, Paris, July 27-29, 1998

Scientific paper

In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an explicit operator construction of the corresponding collective field theory in terms of a bosonic field on a hyperelliptic Riemann surface, with special operators associated with the branch points. The quasiclassical expressions for the spectral kernel and the joint eigenvalue probabilities are then easily obtained as correlation functions of current, fermionic and twist operators. The result for the spectral kernel is valid both in macroscopic and microscopic scales. At the end we briefly consider generalizations in different directions.

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