Elsevier

Nuclear Physics B

Volume 957, August 2020, 115092
Nuclear Physics B

Multi-graded Galilean conformal algebras

https://doi.org/10.1016/j.nuclphysb.2020.115092Get rights and content
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Abstract

Galilean conformal algebras can be constructed by contracting a finite number of conformal algebras, and enjoy truncated Z-graded structures. Here, we present a generalisation of the Galilean contraction procedure, giving rise to Galilean conformal algebras with truncated Zσ-gradings, σN. Detailed examples of these multi-graded Galilean algebras are provided, including extensions of the Galilean Virasoro and affine Kac-Moody algebras. We also derive the associated Sugawara constructions and discuss how these examples relate to multivariable extensions of Takiff algebras. We likewise apply our generalised contraction prescription to tensor products of W3 algebras and obtain new families of higher-order Galilean W3 algebras.

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