Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as W -algebras. Known examples include contractions of pairs of the Virasoro algebra, its N = 1 superconformal extension, or the W 3 algebra. Here, we introduce a contraction prescription of the corresponding operator-product algebras, or equivalently, a prescription for contracting tensor products of vertex algebras. With this, we work out the Galilean conformal algebras arising from contractions of N = 2 and N = 4 superconformal algebras as well as of the W -algebras W (2, 4), W (2, 6), W 4 , and W 5 . The latter results provide evidence for the existence of a whole new class of W -algebras which we call Galilean W -algebras. We also apply the contraction prescription to affine Lie algebras and find that the ensuing Galilean affine algebras admit a Sugawara construction. The corresponding central charge is level-independent and given by twice the dimension of the underlying finite-dimensional Lie algebra. Finally, applications of our results to the characterisation of structure constants in W -algebras are proposed.

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The usual Galilean contraction procedure for generating new conformal symmetry algebras takes as input a number of symmetry algebras which are equivalent up to central charge. We demonstrate that the equivalence condition can be relaxed by inhomogeneously contracting the chiral algebras and present general results for the ensuing asymmetric Galilean algebras. Several examples relevant to conformal field theory are discussed in detail, including superconformal algebras and W-algebras. We also discuss how the Sugawara construction is modified in the asymmetric setting.

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A Galilean contraction is a way to construct Galilean conformal algebras from a pair of infinitedimensional 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.