Emergent non-invertible symmetries in $\mathcal{N}=4$ Super-Yang-Mills theory

Understand

One of the simplest examples of non-invertible symmetries in higher dimensions appears in 4d Maxwell theory, where its $SL(2,\mathbb{Z})$ duality group can be combined with gauging subgroups of its electric and magnetic 1-form symmetries to yield such defects at many different values of the coupling.

• Even though $\mathcal{N}=4$ Super-Yang-Mills (SYM) theory also has an $SL(2,\mathbb{Z})$ duality group, it only seems to share two types of such non-invertible defects with Maxwell theory (known as duality and triality defects).
• Motivated by this apparent difference, we begin our investigation of the fate of these symmetries by studying the case of 4d $\mathcal{N}=4$ $U(1)$ gauge theory which contains Maxwell theory in its content.
• Surprisingly, we find that the non-invertible defects of Maxwell theory give rise, when combined with the standard $U(1)$ symmetry acting on the free fermions, to defects which act on local operators as elements of the $U(1)$ outer-automorphism of the $\mathcal{N}=4$ superconformal algebra, an operation that was referred to in the past as the "bonus symmetry".