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On vertex algebra representations of the Schrödinger-Virasoro Lie algebra.(English)Zbl 1196.81209

Summary: 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 \(\frac{3}{2}\) 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 \(z=2\).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 and its associated vertex operators. We also compute two- and three-point functions of still conjectural massive fields that are defined by an analytic continuation with respect to a formal parameter.

MSC:

17B69 Vertex operators; vertex operator algebras and related structures
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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