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

Abstract

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 ϕ-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 ϕ-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 ϕ-theory and dropping its bosonic part leads us to a purely fermionic theory with subsystem symmetries called ψ-theory. We argue that lattice regularization of the ψ-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 ϕ-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.