Generalized Global Symmetries of $T[M]$ Theories. I

Understand

We study reductions of 6d theories on a $d$-dimensional manifold $M_d$, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting $(6-d)$-dimensional theory $T[M_d]$.

• We refine and generalize the notion of "polarization" to "polarization on $M_d$," which serves to fix the spectrum of local and extended operators in $T[M_d]$.
• Another important feature of theories $T[M_d]$ is that they often possess higher-group symmetries, such as 2-group and 3-group symmetries.
• We study the origin of such symmetries as well as physical implications including symmetry breaking and symmetry enhancement in the renormalization group flow.