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 $\varphi$-theory in $d+1$ dimensions and discuss its properties studied in literature for $d\le 3$ such as self-duality, vacuum structure, 't Hooft anomaly, anomaly inflow and lattice regularization. Next we study a theory called chiral $\varphi$-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 $\varphi$-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 $\varphi$-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.

arXiv comment33 pages, v3

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• Multipole and fracton topological order via gauging foliated SPT phases
• Anomaly inflow for dipole symmetry and higher form foliated field theories
• Electric-Magnetic Duality for Symmetric Tensor Gauge Theories and Immobile $p$-branes
• Matrix product state classification of 1D multipole symmetry protected topological phases
• Exotic theta terms in 2+1d fractonic field theory