Brane webs, $5d$ gauge theories and $6d$ $\mathcal{N}$$=(1,0)$ SCFT's

TL;DR

This paper explores the relationship between 5d gauge theories engineered by brane webs and their corresponding 6d $ ext{SCFT}$s, proposing a method to identify the 6d theories and studying their compactifications.

Contribution

It introduces a new method to determine 6d $ ext{SCFT}$s from 5d gauge theories engineered via brane webs and analyzes their 4d compactifications.

Findings

Proposed a systematic way to identify 6d $ ext{SCFT}$s from 5d theories.

Demonstrated the method with multiple examples.

Discussed implications for 4d theories obtained from 6d compactifications.

Abstract

We study $5d$ gauge theories that go in the UV to $6d$ $\mathcal{N}$$=(1,0)$ SCFT. We focus on these theories that can be engineered in string theory by brane webs. Given a theory in this class, we propose a method to determine the $6d$ SCFT it goes to. We also discuss the implication of this to the compactification of the resulting $6d$ SCFT on a torus to $4d$. We test and demonstrate this method with a variety of examples.