Higher-order Galilean contractions

Abstract

A Galilean contraction is a way to construct Galilean conformal algebras from a pair of infinite-dimensional conformal algebras, or equivalently, a method for contracting tensor products of vertex algebras. Here, we present a generalisation of the Galilean contraction prescription to allow for inputs of any finite number of conformal algebras, resulting in new classes of higher-order Galilean conformal algebras. We provide several detailed examples, including infinite hierarchies of higher-order Galilean Virasoro algebras, affine Kac-Moody algebras and the associated Sugawara constructions, and $W_3$ algebras.

15 pages

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Cited by in corpus (4)

• Non-Lorentzian Kač-Moody Algebras
• On conformal field theories based on Takiff superalgebras
• Multi-graded Galilean conformal algebras
• Asymmetric Galilean conformal algebras