Counting Gauge Invariant Operators in SQCD with Classical Gauge Groups

TL;DR

This paper computes generating functions for gauge invariant operators in supersymmetric QCD with classical gauge groups using advanced mathematical techniques, revealing detailed symmetry and geometric properties of the moduli space.

Contribution

It provides the full character expansion for SQCD with SO and Sp gauge groups and analyzes the geometric structure of the classical moduli space.

Findings

Full character expansion for SO and Sp gauge groups

Moduli space is an irreducible affine Calabi-Yau cone

Orientifold action relates SU, SO, and Sp SQCD

Abstract

We use the plethystic programme and the Molien-Weyl fomula to compute generating functions, or Hilbert Series, which count gauge invariant operators in SQCD with the SO and Sp gauge groups. The character expansion technique indicates how the global symmetries are encoded in the generating functions. We obtain the full character expansion for each theory with arbitrary numbers of colours and flavours. We study the orientifold action on SQCD with the SU gauge group and examine how it gives rise to SQCD with the SO and Sp gauge groups. We establish that the classical moduli space of SQCD is not only irreducible, but is also an affine Calabi-Yau cone over a weighted projective variety.