Asymmetric Galilean conformal algebras

TL;DR

This paper introduces asymmetric Galilean conformal algebras by relaxing the usual symmetry equivalence condition, exploring their structure, examples, and modifications to the Sugawara construction relevant to conformal field theory.

Contribution

It presents a novel asymmetric contraction method for conformal algebras, expanding the class of Galilean conformal symmetries beyond traditional symmetric cases.

Findings

Constructed asymmetric Galilean conformal algebras from chiral algebras.

Analyzed examples including superconformal and W-algebras.

Modified the Sugawara construction for the asymmetric setting.

Abstract

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.