On Continuous 2-Category Symmetries and Yang-Mills Theory

Understand

We study a 4d gauge theory $U(1)^{N-1}\rtimes S_N$ obtained from a $U(1)^{N-1}$ theory by gauging a 0-form symmetry $S_N$.

• We show that this theory has a global continuous 2-category symmetry, whose structure is particularly rich for $N>2$.
• This example allows us to draw a connection between the higher gauging procedure and the difference between local and global fusion, which turns out to be a key feature of higher category symmetries.
• By studying the spectrum of local and extended operators, we find a mapping with gauge invariant operators of 4d $SU(N)$ Yang-Mills theory.