On the 6d Origin of Non-invertible Symmetries in 4d

TL;DR

This paper explores how six-dimensional (2,0) superconformal theories can be used to construct four-dimensional theories featuring non-invertible symmetries, including new examples with M-ality defects of prime power order.

Contribution

It introduces a novel application of 6d (2,0) theories to generate 4d theories with non-invertible symmetries and M-ality defects, expanding the known landscape.

Findings

Recovered known results on non-invertible symmetries

Constructed infinitely many new 4d theories with M-ality defects

Provided examples with order M=p^k, p prime

Abstract

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.