Hilbert Series for Theories with Aharony Duals

TL;DR

This paper computes the Hilbert series for 3d N=2 supersymmetric gauge theories with Aharony duals, revealing detailed algebraic structures of their moduli spaces by extending techniques from 3d N=4 theories.

Contribution

It extends Coulomb branch Hilbert series methods from 3d N=4 to 3d N=2 theories, providing a general algebraic expression for moduli spaces with Aharony duals.

Findings

Derived a general Hilbert series formula for moduli spaces

Analyzed the components of the moduli space in detail

Connected algebraic structures to gauge theory dualities

Abstract

The algebraic structure of moduli spaces of 3d N=2 supersymmetric gauge theories is studied by computing the Hilbert series which is a generating function that counts gauge invariant operators in the chiral ring. These U(N_c) theories with N_f flavors have Aharony duals and their moduli spaces receive contributions from both mesonic and monopole operators. In order to compute the Hilbert series, recently developed techniques for Coulomb branch Hilbert series in 3d N=4 are extended to 3d N=2. The Hilbert series computation leads to a general expression of the algebraic variety which represents the moduli space of the U(N_c) theory with N_f flavors and its Aharony dual theory. A detailed analysis of the moduli space is given, including an analysis of the various components of the moduli space.