W-Algebras Extending Affine gl(1|1)

Abstract: It was recently shown that gl^1|1 admits an infinite family of simple current extensions. Here, these findings are reviewed and explicit free field realisations of the extended algebras are constructed. The leading contributions to the operator product algebra are then calculated. Among these extensions, one finds four infinite families that seem to contain, as subalgebras, copies of the W^2_N algebras of Feigin and Semikhatov at various levels and central charges +/- 1.