HAL : hal-00487221, version 1

arXiv : 1005.4730

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Duality and replicas for a unitary matrix model

E. Brezin 1, S. Hikami

(26/05/2010)

In a generalized Airy matrix model, a power $p$ replaces the cubic term of the Airy model introduced by Kontsevich. The parameter $p$ corresponds to Witten's spin index in the theory of intersection numbers of moduli space of curves. A continuation in $p$ down to $p= -2$ yields a well studied unitary matrix model, which exhibits two different phases in the weak and strong coupling regions, with a third order critical point in-between. The application of duality and replica to the $p$-th Airy model allows one to recover both the weak and strong phases of the unitary model, and to establish some new results for these expansions. Therefore the unitary model is also indirectly a generating function for intersection numbers.

1 :	Laboratoire de Physique Théorique de l'ENS (LPTENS)
	CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris

Domaine

:

Physique/Physique des Hautes Energies - Théorie Physique/Physique mathématique Mathématiques/Physique mathématique

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Contributeur : Edouard Brézin <>

Soumis le : Vendredi 28 Mai 2010, 13:29:45

Dernière modification le : Vendredi 28 Mai 2010, 13:29:45