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.

18 pages, LaTeX

References in corpus (3)

• Classification of Two Dimensional N=4 Superconformal Symmetries
• Constructing Classical and Quantum Superconformal Algebras on the Boundary of AdS_3
• Unitary Representations of Some Infinite Dimensional Lie Algebras Motivated by String Theory on AdS_3

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• Second order splitting functions and infrared safe cross sections in $\mathcal{N}=4$ SYM theory
• A non-reductive N=4 superconformal algebra
• A note on Kerr/CFT and free fields
• Asymmetric Galilean conformal algebras
• Shadows and Twisted Variables