The determination of the exact BPS spectrum of a (large class of) four–dimensional N=2 QFT’s is equivalent to the Representation Theory of certain associative algebras, namely the path algebras of quivers bounded by the Jacobian ideal of a superpotential W. In this contest there is a detailed dictionary between QFT and Representation Theory. Properties which are elementary on one side are tipically subtle and hard to prove in the other. Hence both subjects have something to learn from the correspondence.
