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 Poincare 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 (delocalised) 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.