Loop Equations from Differential Systems on Curves

Raphaël Belliard (1) , Bertrand Eynard (1) , Olivier Marchal (2, 3)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 ICJ - Institut Camille Jordan
3 PSPM - Probabilités, statistique, physique mathématique

To any flat section equation of the form ∇ 0Ψ = Φ Ψ in a principal bundle over a Riemann surface (∇ 0 is a reference connection), we associate an infinite sequence of “correlators”, symmetric n-differentials on Σ that we denote { W- n} n ∈ N. The goal of this article is to prove that these correlators are solutions to “loop equations,” the same ones satisfied by correlation functions in random matrix models, or equivalently Ward identities of Virasoro or W-symmetric CFT. © 2017, Springer International Publishing AG, part of Springer Nature.

Mots clés: random matrix models

Domaines: Physique [physics]

Raphaël Belliard, Bertrand Eynard, Olivier Marchal. Loop Equations from Differential Systems on Curves. Annales Henri Poincaré, 2017, 19 (1), pp.141-161. ⟨10.1007/s00023-017-0622-x⟩. ⟨cea-04523134⟩