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Breakdown of universality in multi-cut matrix models

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arxiv cond-mat/0003324 v2 pith:O3A5MZRV submitted 2000-03-20 cond-mat hep-th

Gabrielle Bonnet , Francois David , Bertrand Eynard This is my paper · ORCID
classification cond-mathep-th
keywords correlatorsexpansionfieldlargemeannumberorthogonalpolynomials
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We solve the puzzle of the disagreement between orthogonal polynomials methods and mean field calculations for random NxN matrices with a disconnected eigenvalue support. We show that the difference does not stem from a Z2 symmetry breaking, but from the discreteness of the number of eigenvalues. This leads to additional terms (quasiperiodic in N) which must be added to the naive mean field expressions. Our result invalidates the existence of a smooth topological large N expansion and some postulated universality properties of correlators. We derive the large N expansion of the free energy for the general 2-cut case. From it we rederive by a direct and easy mean-field-like method the 2-point correlators and the asymptotic orthogonal polynomials. We extend our results to any number of cuts and to non-real potentials.

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Cited by 2 Pith papers

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  1. Phases in WLZZ Matrix Models

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    For WLZZ two-matrix models, integration contours describe only a finite-N subspace of Ward identity solutions, and the full solution space is recovered only in the N-to-infinity limit.

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    Negative-tension ZZ-branes are required by resurgence to build complete transseries for minimal-string free energies, with analytic Stokes data and extensions to JT gravity and other string models.

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