Hilbert Series and Superconformal Indices of the Improved Bifundamentals

TL;DR

This paper investigates the moduli space structure of Improved Bifundamentals superconformal field theories using Hilbert Series, revealing their moduli spaces are irreducible and connected, contrasting with typical SCFTs.

Contribution

It introduces a novel analysis of the moduli space of Improved Bifundamentals using Hilbert Series, showing these spaces are irreducible and connected.

Findings

Moduli spaces are irreducible algebraic varieties.

Moduli spaces have a single connected component.

Hilbert Series is used as a limit of the Superconformal Index.

Abstract

We explore the structure of the moduli space of vacua of Improved Bifundamentals, a recently introduced class of superconformal field theories. Utilizing the Hilbert Series, computed as a specific limit of the Superconformal Index, we establish that the moduli spaces of these theories are irreducible algebraic varieties, presenting a single connected component as opposed to the more common scenario of multiple intersecting branches found in typical SCFT moduli spaces.