Dualities of 5d gauge theories from S-duality

TL;DR

This paper introduces a geometric method to systematically identify dualities in 5d supersymmetric gauge theories, revealing a broad class of previously known and new irreducible dualities through S-duality transformations.

Contribution

It develops a geometric approach to determine irreducible dualities in 5d gauge theories, generalizing many known dualities by adding matter and analyzing Dynkin diagrams.

Findings

Systematic construction of irreducible dualities

Classification of dualities via Dynkin diagram modifications

Extension of known 5d dualities

Abstract

We describe a general method to determine dualities between supersymmetric 5d gauge theories. The method is based on performing local S-dualities in the geometry associated to the gauge theory. We find that often a duality can be obtained by adding matter to both sides of a more primitive duality. This allows us to define the notion of irreducible dualities which cannot be obtained from more primitive dualities. More general dualities then are obtained by adding matter to both sides of an irreducible duality. The geometric method described in this paper allows us to systematically construct irreducible dualities. As an application, we explicitly determine a special class of irreducible dualities classified by removal and addition of edges into a Dynkin diagram. This class of dualities vastly generalizes many of the known 5d dualities in the literature.