Publication : t08/140

Topological expansion of the Bethe ansatz, and non-commutative algebraic geometry

Eynard B. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Marchal O. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Abstract:
In this article, we define a non-commutative deformation of the "symplectic invariants" of an algebraic hyperelliptical plane curve. The necessary condition for our definition to make sense is a Bethe ansatz. The commutative limit reduces to the symplectic invariants, i.e. algebraic geometry, and thus we define non-commutative deformations of some algebraic geometry quantities. In particular our non-commutative Bergmann kernel satisfies a Rauch variational formula. Those non-commutative invariants are inspired from the large N expansion of formal non-hermitian matrix models. Thus they are expected to be related to the enumeration problem of discrete non-orientable surfaces of arbitrary topologies.
Année de publication : 2009
Revue : JHEP 0903 094 (2009)
DOI : 10.1088/1126-6708/2009/03/094
Preprint : arXiv:0809.3367
Langue : Anglais

Fichier(s) à télécharger :
  • 1126-6708_2009_03_094.pdf
  • publi.pdf

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