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

Bertrand Eynard (1)

1 SPhT - Service de Physique Théorique

The loop equations for a chain of hermitian random matrices arecomputed explicitely, including the 1/N^2 corrections.To leading order, the master loop equation reduces to analgebraic equation, whose solution can be written in terms ofgeometric 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/N^2 expansion.

Mots clés: large N; topological; free energy; random matrix; loop equations; dispesionless Toda; boundary operators; correlation functions

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Bertrand Eynard. Master loop equations, free energy and correlations for the chain of matrices.. 2003. ⟨hal-00000572v2⟩