On the 6d origin of non-invertible symmetries in 4d

A bstract It is well-known that six-dimensional superconformal field theories can be exploited to unravel interesting features of lower-dimensional theories obtained via compactifications. In this short note we discuss a new application of 6d (2,0) theories in constructing 4d theories with Kramers-Wannier-like non-invertible symmetries. Our methods allow to recover previously known results, as well as to exhibit infinitely many new examples of four dimensional theories with “M-ality” defects (arising from operations of order M generalizing dualities). In particular, we obtain examples of order M = p k , where p > 1 is a prime number and k is a positive integer.