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

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