2007/03/08 by Jérémie Unterberger, Unterberger, Jeremie
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.cond-mat/0703214
openalex publication_date 2007/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Schrödinger-Virasoro Lie algebra \mathfraksv 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 \mathfraksv 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.