Another algebraic variational principle for the spectral curve of matrix models

Bertrand Eynard (1, 2)

1 CRM - Centre de Recherches Mathématiques [Montréal]
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We propose an alternative variational principle whose critical point is the algebraic plane curve associated to a matrix model (the spectral curve, i.e. the large $N$ limit of the resolvent). More generally, we consider a variational principle that is equivalent to the problem of finding a plane curve with given asymptotics and given cycle integrals. This variational principle is not given by extremization of the energy, but by the extremization of an "entropy".

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]

Bertrand Eynard. Another algebraic variational principle for the spectral curve of matrix models. 2016. ⟨cea-01277989⟩