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In theoretical physics, a short supermultiplet is a supermultiplet i.e. a representation of the supersymmetry algebra whose dimension is smaller than where is the number of real supercharges. The representations that saturate the bound are known as the long supermultiplets. [1]
The states in a long supermultiplet may be produced from a representative by the action of the lowering and raising operators, assuming that for any basis vector, either the lowering operator or its conjugate raising operator produce a new nonzero state. This is the reason for the dimension indicated above. On the other hand, the short supermultiplets admit a subset of supercharges that annihilate the whole representation. That is why the short supermultiplets contain the BPS states, another description of the same concept. [2]
The BPS states are only possible for objects that are either massless or massive extremal, i.e. carrying a maximum allowed value of some central charges.
