Killing superalgebra deformations of ten-dimensional supergravity backgrounds

We explore Lie superalgebra deformations of the Killing superalgebras of some ten-dimensional supergravity backgrounds. We prove the rigidity of the Poincaré superalgebras in types I, IIA and IIB, as well as of the Killing superalgebra of the Freund-Rubin vacuum of type IIB supergravity. We also prove rigidity of the Killing superalgebras of the NS5-, D0-, D3-, D4- and D5-branes, whereas we exhibit the possible deformations of the D1-, D2-, D6- and D7-brane Killing superalgebras, as well as of that of the type II fundamental string solutions. We relate the superalgebra deformations of the D2- and D6-branes to those of the (delocalized) M2-brane and the Kaluza-Klein monopole, respectively. The good behaviour under Kaluza-Klein reduction suggests that the deformed superalgebras ought to have a geometric interpretation.