Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d+1 dimensions

Understand

We study various non-relativistic field theories with exotic symmetries called subsystem symmetries, which have recently attracted much attention in the context of fractons.

• We start with a scalar theory called $\phi$-theory in $d+1$ dimensions and discuss its properties studied in literature for $d\leq 3$ such as self-duality, vacuum structure, 't Hooft anomaly, anomaly inflow and lattice regularization.
• Next we study a theory called chiral $\phi$-theory which is an analogue of a chiral boson with subsystem symmetries.
• Then we discuss theories including fermions with subsystem symmetries.