Non-Invertible Symmetries of $\mathcal{N}=4$ SYM and Twisted Compactification

TL;DR

This paper explores how non-invertible symmetries in 4d $ abla=4$ super-Yang-Mills can be used to generate new 3d $ abla=6$ theories through twisted compactification, expanding the landscape of possible RG flows.

Contribution

It introduces the concept of non-invertible twisted compactification and demonstrates its ability to produce novel 3d theories from 4d $ abla=4$ SYM.

Findings

Non-invertible symmetries descend from Montonen-Olive duality.

Twisted compactification by non-invertible symmetries yields new 3d $ abla=6$ theories.

These theories are inaccessible via invertible symmetry twists.

Abstract

Non-invertible symmetries have recently been understood to provide interesting contraints on RG flows of QFTs. In this work, we show how non-invertible symmetries can also be used to generate entirely new RG flows, by means of so-called "non-invertible twisted compactification". We illustrate the idea in the example of twisted compactifications of 4d $\mathcal{N}=4$ super-Yang-Mills (SYM) to three dimensions. After giving a catalogue of non-invertible symmetries descending from Montonen-Olive duality transformations of 4d $\mathcal{N}=4$ SYM, we show that twisted compactification by non-invertible symmetries can be used to obtain 3d $\mathcal{N}=6$ theories which appear otherwise unreachable if one restricts to twists by invertible symmetries.