# Towards Classification of 5d SCFTs: Single Gauge Node

## TL;DR

This paper develops criteria for classifying 5d superconformal field theories arising from gauge theories, focusing on classical and exceptional groups, and identifies new classes of SCFTs based on these criteria.

## Contribution

It introduces a set of consistency criteria for 5d SCFTs and applies them to classify theories from simple gauge groups, revealing new classes especially at lower ranks.

## Key findings

- Large rank classical groups have SCFTs with linearly growing matter bounds.
- Additional SCFT cases found for classical groups of rank ≤ 8.
- Classification of allowed matter content for all exceptional groups.

## Abstract

We propose a number of apparently equivalent criteria necessary for the consistency of a 5d SCFT in its Coulomb phase and use these criteria to classify 5d SCFTs arising from a gauge theory with simple gauge group. These criteria include the convergence of the 5-sphere partition function; the positivity of particle masses and monopole string tensions; and the positive definiteness of the metric in some region in the Coulomb branch. We find that for large rank classical groups simple classes of SCFTs emerge where the bounds on the matter content and the Chern-Simons level grow linearly with rank. For classical groups of rank less than or equal to 8, our classification leads to additional cases which do not fit in the large rank analysis. We also classify the allowed matter content for all exceptional groups.