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

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 <= 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. We first construct a supersymmetric version of the phi-theory and dropping its bosonic part leads us to a purely fermionic theory with subsystem symmetries called psi-theory. We argue that lattice regularization of the psi-theory generically suffers from an analogue of doubling problem as previously pointed out in the d = 3 case. We propose an analogue of Wilson fermion to avoid the doubling problem. We also supersymmetrize the chiral phi-theory and dropping the bosonic part again gives us a purely fermionic theory. We finally discuss vacuum structures of the theories with fermions and find that they are infinitely degenerate because of spontaneous breaking of subsystem symmetries.

Automated summary

In this paper, we investigate various non-relativistic field theories with exotic symmetries called subsystem symmetries. We study scalar theories, chiral scalar theories, and theories with fermions. The vacuum structures and lattice regularization of these theories are discussed. Moreover, we find that the vacuum structures of theories with fermions are infinitely degenerate due to the spontaneous breaking of subsystem symmetries.