Rational differential systems, loop equations, and application to the q-th reductions of KP - Archive ouverte HAL Access content directly
Journal Articles Annales Henri Poincaré Year : 2015

Rational differential systems, loop equations, and application to the q-th reductions of KP

Abstract

To any solution of a linear system of differential equations, we associate a kernel, correlators satisfying a set of loop equations, and in presence of isomonodromic parameters, a Tau function. We then study their semiclassical expansion (WKB type expansion in powers of the weight hbar per derivative) of these quantities. When this expansion is of topological type (TT), the coefficients of expansions are computed by the topological recursion with initial data given by the semiclassical spectral curve of the linear system. This provides an efficient algorithm to compute them at least when the semiclassical spectral curve is of genus 0. TT is a non trivial property, and it is an open problem to find a criterion which guarantees it is satisfied. We prove TT and illustrate our construction for the linear systems associated to the q-th reductions of KP - which contain the (p,q) models as a specialization.
Fichier principal
Vignette du fichier
beboey1.pdf (756.14 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

cea-01117895 , version 1 (18-10-2022)

Identifiers

Cite

Michel Bergère, Gaëtan Borot, Bertrand Eynard. Rational differential systems, loop equations, and application to the q-th reductions of KP. Annales Henri Poincaré, 2015, 16, pp.2713-2782. ⟨10.1007/s00023-014-0391-8⟩. ⟨cea-01117895⟩
77 View
3 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More