HAL : hal-00135660, version 2

arXiv : cond-mat/0703214

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v1 (08-03-2007)

v2 (09-03-2007)

On vertex algebra representations of the Schrödinger-Virasoro Lie algebra.

Jeremie Unterberger 1

(08/03/2007)

The Schrödinger-Virasoro Lie algebra \mathfrak{sv} is an extension of the Virasoro Lie algebra by a nilpotent Lie algebra formed with a bosonic current of weight 3/2 and a bosonic current of weight 1. It is also a natural infinite-dimensional extension of the Schrödinger Lie algebra, which -leaving aside the invariance under time-translation - has been proved to be a symmetry algebra for many statistical physics models undergoing a dynamics with dynamical exponent z=2; it should consequently play a role akin to that of the Virasoro Lie algebra in two-dimensional equilibrium statistical physics. We define in this article general Schrödinger-Virasoro primary fields by analogy with conformal field theory, characterized by a 'spin' index and a (non-relativistic) mass, and construct vertex algebra representations of \mathfrak{sv} out of a charged symplectic boson and a free boson. We also compute two- and three-point functions of still conjectural massive fields that are defined by analytic continuation with respect to a formal parameter.

1 :	Institut Elie Cartan Nancy (IECN)
	CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)

Domaine

:

Physique/Matière Condensée/Mécanique statistique Physique/Physique mathématique

Mots Clés : conformal field theory – correlation functions – algebraic structure of integrable models – Schrödinger invariance – supersymmetry – non-equilibrium statistical physics – infinite-dimensional Lie algebras

hal-00135660, version 2

http://hal.archives-ouvertes.fr/hal-00135660

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Contributeur : Jeremie Unterberger <>

Soumis le : Vendredi 9 Mars 2007, 10:52:31

Dernière modification le : Vendredi 9 Mars 2007, 10:55:25