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

TL;DR

This paper extends the $AdS_{5} imes S^{5}$ superalgebra to include string and brane charges, revealing a large nonunitary representation with 899 complex brane charges and explicit super-commutators.

Contribution

It introduces a noncentral extension of the superalgebra incorporating brane charges and provides a complete classification and explicit structure of these charges.

Findings

899 complex brane charges identified

Explicit super-commutators derived

Nonunitary representation characterized

Abstract

We propose an extension of the su(2,2|4) superalgebra to incorporate the $F1/D1$ string charges in type IIB string theory on the $AdS_{5} \times S^{5}$ 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.