Giant gravitons, Bogomol'nyi-Prasad-Sommerfield bounds, and noncommutativity - art. no. 044001

It has been recently suggested that gravitons moving in AdS(m)xS(n) spaceti mes along the S-n blow up into spherical (n - 2)-branes whose radius increa ses with increasing angular momentum. This leads to an upper bound on the a ngular momentum, thus ''explaining'' the stringy exclusion principle. We sh ow that this bound is present only for states which saturate a BPS-like con dition involving the energy E and angular momentum J,E greater than or equa l toJ/R, where R is the radius of S-n. Restriction of motion to such states lead to a noncommutativity of the coordinates on S-n. As an example of mot ions which do not obey the exclusion principle bound, we show that there ar e finite action instanton configurations interpolating between two possible BPS states. We suggest that this is consistent with the proposal that ther e is an effective description in terms of supergravity defined on noncommut ative spaces and noncommutativity arises here because of imposing supersymm etry.