Comments on N=4 Superconformal Algebras

Abstract

We present a new and asymmetric N=4 superconformal algebra for arbitrary central charge, thus completing our recent work on its classical analogue with vanishing central charge. Besides the Virasoro generator and 4 supercurrents, the algebra consists of an internal SL(2) \otimes U(1) Kac-Moody algebra in addition to two spin 1/2 fermions and a bosonic scalar. The algebra is shown to be invariant under a linear twist of the generators, except for a unique value of the continuous twist parameter. At this value, the invariance is broken and the algebra collapses to the small N=4 superconformal algebra. In the context of string theory, the asymmetric N=4 superconformal algebra is provided with an explicit construction on the boundary of AdS_3, and is induced by an affine SL(2|2) current superalgebra residing on the world sheet. Substituting the world sheet SL(2|2) by the coset SL(2|2)/U(1) results in the small N=4 superconformal algebra on the boundary of AdS_3.