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Vincent Bouchard; Bertrand Eynard
Reconstructing WKB from topological recursion
(De la récurrence topologique à WKB)
Journal de l'École polytechnique — Mathématiques, 4 (2017), p. 845-908, doi: 10.5802/jep.58
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Class. Math.: 14H70, 81Q20, 81S10, 30F30
Mots clés: Récurrence topologique, WKB, courbes quantiques, quantification

Résumé - Abstract

Nous montrons que la récurrence topologique permet de reconstruire le développement WKB d’une courbe quantique pour toutes les courbes spectrales dont les polygones de Newton n’ont pas de point intérieur (et qui sont lisses en tant que courbes affines). Cette classe de courbes contient presque toutes les courbes quantiques déjà étudiées dans la littérature, ainsi que beaucoup d’autres ; en particulier, beaucoup de courbes d’ordre plus élevé que $2$ sont incluses dans cette classe. Nous étudions aussi la relation entre le choix d’un ordre pour la quantification de la courbe spectrale et le choix d’un diviseur pour l’intégration nécessaire à la reconstruction du développement WKB.

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