Geometry

Physics

Pure mathematics

Mathematics

Mathematical physics

Quantum mechanics

Homogeneous space

Compactification (mathematics)

Invertible matrix

Journal of High Energy Physics

A bstract 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 super-Yang-Mills (SYM) to three dimensions. After giving a catalogue of non-invertible symmetries descending from Montonen-Olive duality transformations of 4d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM, we show that twisted compactification by non-invertible symmetries can be used to obtain 3d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 6 theories which appear otherwise unreachable if one restricts to twists by invertible symmetries.

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