Non-invertible symmetries of $$ \mathcal{N} $$ = 4 SYM and twisted compactification

Abstract

Abstract Non-invertible symmetries have recently been understood to provide interesting constraints 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 $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 4 SYM, we show that twisted compactification by non-invertible symmetries can be used to obtain 3d $$ \mathcal{N} $$ N = 6 theories which appear otherwise unreachable if one restricts to twists by invertible symmetries.