18.11.2015 (Wednesday)

Polygon Seminar: An introduction to the Hilbert series as operator counting

Triangular Seminar Diego Rodriguez-Gomez (University of Oviedo)

15:00 QMW
room GO Jones 610

Counting operators in supersymmetric field theories is very interesting, as the corresponding generating functions encode properties of the field theory. In this lecture we will mostly concentrate on 4d SUSY field theories. After reviewing some basic notions about SUSY field theories leading to the notion of chiral ring, we will introduce a generating function enumerating operators in the ring. This function is the so-called Hilbert series. In the case of SCFTs with a gravity dual, we will show how this function recovers geometric properties of the dual gravity background. The uses of the Hilbert series go beyond this, since, as we will see, being a counting of operators, it is of relevance in the computation of instanton partition functions for pure gauge theories. In the second part of the lecture we will briefly touch upon these issues.