Complete prepotential for 5d $\mathcal{N}=1$ superconformal field theories

TL;DR

This paper introduces a comprehensive prepotential for 5d ${ m N}=1$ superconformal field theories that captures perturbative aspects, global symmetries, and is applicable across parameter spaces, with explicit examples.

Contribution

It proposes a complete prepotential framework for 5d ${ m N}=1$ SCFTs that unifies various gauge theory realizations and reveals global symmetries.

Findings

Constructed the complete prepotential for specific 5d gauge theories.

Demonstrated the prepotential's invariance under dualities.

Applied the framework to multiple gauge theories with various flavors.

Abstract

For any 5d ${\cal N}=1$ superconformal field theory, we propose a "complete" prepotential which reduces to the perturbative prepotential for any of its possible gauge theory realizations, manifests its global symmetry when written in terms of the invariant Coulomb branch parameters, and is valid for the whole parameter region. As concrete examples, we consider $SU(2)$ gauge theories with up to 7 flavors, $Sp(2)$ gauge theories with up to 9 flavors, and $Sp(2)$ gauge theories with 1 antisymmetric tensor and up to 7 flavors, as well as their dual gauge theories.