One of the simplest examples of noninvertible symmetries in higher dimensions appears in 4D Maxwell theory, where its $\mathrm{SL}(2,\mathbb{Z})$ 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 $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory also has an $\mathrm{SL}(2,\mathbb{Z})$ duality group, it only seems to share two types of such noninvertible 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 noninvertible defects of Maxwell theory give rise, when combined with the standard U(1) symmetry acting on the free fermions, to defects that 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.” Turning to the non-Abelian case of $\mathcal{N}=4$ SYM theory, the bonus symmetry is not an exact symmetry of the theory, but is known to emerge at the supergravity limit. Based on this observation, we study this limit and show that, if it is taken in a certain way, noninvertible defects that realize different elements of the bonus symmetry emerge as approximate symmetries, in analogy to the Abelian case.

• Received 28 January 2024
• Accepted 22 April 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.201601

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Published by the American Physical Society