The spacetime superalgebras from M-branes in M-brane backgrounds

We derive the spacetime superalgebras explicitly from “test” M-brane actions in M-brane backgrounds to the lowest order in θ via canonical formalism, and discuss various BPS saturated configurations on the basis of their central charges which depend on the harmonic functions determined by the backgrounds. All the 1/4 supersymmetric intersections of two M-branes obtained previously are deduced from the requirement of the test branes to be so “gauge fixed” in the brane backgrounds as to preserve 1/4 supersymmetry. Furthermore, some of 1/2-supersymmetric bound states of two M-branes are deduced from the behavior of the harmonic functions in the limits of vanishing distances of the two branes. The possibilities of some triple intersections preserving 1/4 supersymmetry are also discussed.