The supersymmetric affine Yangian

The affine Yangian of gl1 is known to be isomorphic to W1+∞, the W-algebra that characterizes the bosonic higher spin — CFT duality. In this paper we propose some of the defining relations of the Yangian that are relevant for the N=2 superconformal version of W1+∞. Our construction is based on the observation that the N=2 superconformal W1+∞ algebra contains two commuting bosonic W1+∞ algebras, and that the additional generators transform in bi-minimal representations with respect to these two algebras. The corresponding affine Yangian can therefore be built up from two affine Yangians of gl1 by adding in generators that transform appropriately.ISSN:1126-6708ISSN:1029-847