Invasion of the giant gravitons from anti-de Sitter space

It has been known for some time that the AdS/CFT correspondence predicts alimit on the number of single particle states propagating on the compactspherical component of the AdS-times-sphere geometry. The limit is called thestringy exclusion principle. The physical origin of this effect has beenobscure but it is usually thought of as a feature of very small distancephysics. In this paper we will show that the stringy exclusion principle is dueto a surprising large distance phenomenon. The massless single particle statesbecome progressively less and less point-like as their angular momentumincreases. In fact they blow up into spherical branes of increasing size. Theexclusion principle is simply understood as the condition that the particleshould not be bigger than the sphere that contains it.Comment: 13 pages, latex; v2: spelled correctly the name of an eminent relativist; v3: comments about AdS_3 corrected, analysis of spherical branes improved, references added; v4: JHEP versio