Counting BPS Operators in the Chiral Ring—the Plethystic Story

摘要

A new method for analyzing supersymmetric gauge theories is presented. This method relies on the counting of all the chiral operators in the chiral ring of a supersymmetric gauge theory. The counting is done by computing a generating function which counts all possible BPS operators that carry a specified set of global U(1) charges. Remarkably, if the supersymmetric gauge theory lives on N D3 brane in Type IIB string theory, exact results for any number of D3 branes can be written down in a concise and elegant fashion. The paper summarizes results from published work in [1,2,3].