Comments on \(N=4\) superconformal algebras (Q1589896)

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 \(SU(2)\otimes U(1)\) 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. The asymmetric \(N=4\) superconformal algebra may be seen as induced by an affine \(SL(2|2)\) current superalgebra. Replacing \(SL(2|2)\) with the coset \(SL(2|2)/U(1),\) results directly in the small \(N=4\) superconformal algebra.