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

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dc.creatorEynard, Bertrand
dc.creatorMarchal, Olivier
dc.date2008-09-19
dc.date.accessioned2026-07-07T12:56:42Z
dc.date.available2026-07-07T12:56:42Z
dc.descriptionIn 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.
dc.descriptionLatex, 59 pages
dc.identifierhttps://arxiv.org/abs/0809.3367
dc.identifierhttp://arxiv.org/abs/0809.3367
dc.identifierJHEP 0903:094,2009
dc.identifierdoi:10.1088/1126-6708/2009/03/094
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224676
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.titleTopological expansion of the Bethe ansatz, and non-commutative algebraic geometry
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