Noncentral extension of the $Ad{S}_5\times S^5$ superalgebra: supermultiplet of brane charges

We propose an extension of the su(2,2|4) superalgebra to incorporate the $F1\mathrm{/}D1$ string charges in type IIB string theory on the $Ad{S}_5\times S^5$ background, or the electro-magnetic charges in the dual super Yang-Mills theory. With the charges introduced, the superalgebra inevitably undergoes a noncentral extension, as noted recently in [1]. After developing a group theoretical method of obtaining the noncentral extension, we show that the charges form a certain nonunitary representation of the original unextended superalgebra, subject to some constraints. We solve the constraints completely and show that, apart from the su(2,2|4) generators, there exist 899 complex brane charges in the extended algebra. Explicitly we present all the super-commutators among them.