Master loop equations, free energy and correlations for the chain of matrices

2003/09/30 by Bertrand Eynard, B Eynard
Computer Science · Physics and Astronomy · #Matrix Theory and Algorithms #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #hep-th

paper · pdf · doi:10.1088/1126-6708/2003/11/018

published as JHEP 0311 (2003) 018 · latex, 1 figure .eps. Misprints corrected, references added

arxiv created 2003/10/30 · openalex publication_date 2003/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

The loop equations for a chain of hermitian random matrices are computed explicitely, including the 1/N² corrections. To leading order, the master loop equation reduces to an algebraic equation, whose solution can be written in terms of geometric properties of the underlying algebraic curve. In particular we compute the free energy, the resolvents, the 2-loop functions and some mixed one loop functions. We also initiate the calculation of the 1/N² expansion.

Citations

• Boundary correlators in 2D quantum gravity: Liouville versus discrete approach
• Breakdown of universality in multi-cut matrix models