SL$(2,\mathbb{Z})$ action on quantum field theories with U(1) subsystem symmetry

Understand

We consider SL$(2,\mathbb{Z})$ action on quantum field theories with U(1) subsystem symmetry in five dimensions.

• This is an analog of the SL$(2,\mathbb{Z})$ action considered in arXiv:hep-th/0307041.
• We show that the exotic level 1 BF theory and the exotic level 1 Chern-Simons theories are trivial and almost trivial, respectively.
• By using this fact, we define S operation and T operation.