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.

33 pages, v3

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Cited by in corpus (7)

• Subsystem Non-Invertible Symmetry Operators and Defects
• Foliated BF theories and Multipole symmetries
• 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