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.

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N=4 超对称杨-米尔斯理论中的涌现不可逆对称性

高维中不可逆对称性最简单的例子之一出现在 4D 麦克斯韦理论中，其中$\mathrm{SL}（2,\mathbb{Z}）$对偶群可以与其电和磁 1 型对称性的测量子群相结合，以在许多不同的耦合值下产生此类缺陷。虽然$\mathcal{氮}=4$超对称杨-米尔斯 (SYM) 理论也有$\mathrm{SL}（2,\mathbb{Z}）$对偶群，它似乎只与麦克斯韦理论共享两种类型的不可逆缺陷（称为对偶缺陷和三重缺陷）。受这种明显差异的启发，我们通过研究 4D 的情况开始研究这些对称性的命运$\mathcal{氮}=4$U(1)规范理论，其内容包含麦克斯韦理论。令人惊讶的是，我们发现麦克斯韦理论的不可逆缺陷与作用于自由费米子的标准 U(1) 对称性相结合，产生了作用于局部算子的缺陷，作为 U(1) 外自同构的元素$\mathcal{氮}=4$超共形代数，过去被称为“奖励对称性”的运算。转向非阿贝尔情况$\mathcal{氮}=4$SYM 理论中，奖金对称性并不是该理论的精确对称性，但已知会在超重力极限下出现。基于这一观察，我们研究了这个极限，并表明，如果以某种方式采取，实现红利对称性不同元素的不可逆缺陷会表现为近似对称性，类似于阿贝尔情况。