4d N=1 dualities from 5d dualities

TL;DR

This paper establishes a method to derive 4d N=1 dualities from 5d KK dualities, linking higher-dimensional gauge theories to lower-dimensional dual pairs and verifying their consistency through anomaly matching and Seiberg dualities.

Contribution

It introduces a systematic prescription to obtain 4d N=1 quiver dualities from 5d dualities, expanding the understanding of dualities across dimensions.

Findings

4d dualities can be derived from 5d KK dualities.

Matching of global symmetry anomalies confirms dualities.

Sequential Seiberg dualities can prove some 4d dualities.

Abstract

We consider $5d$ KK dualities, that is multiple $5d$ gauge theories with the same $6d$ infinite coupling limit. We provide a prescription to associate $4d$ $N=1$ quivers to the $5d$ dual quivers, such that the $4d$ quivers are also dual to each other. The $4d$ dualities are infrared dualities which can be checked matching global symmetry anomalies and in certain cases can be proven using basic Seiberg dualities sequentially. We also consider dualities obtained by Higgsing in two different ways the same $5d$ theory, in some simple examples.