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

TL;DR

This paper explores scalar, fermionic, and supersymmetric field theories with subsystem symmetries in various dimensions, analyzing their properties, anomalies, lattice regularization issues, and vacuum structures, with implications for fracton physics.

Contribution

It introduces new fermionic and supersymmetric theories with subsystem symmetries and addresses lattice regularization challenges like fermion doubling.

Findings

Identification of vacuum degeneracy due to spontaneous symmetry breaking.

Proposal of a Wilson fermion analogue to mitigate doubling problems.

Analysis of anomalies and lattice regularization issues in subsystem symmetric theories.

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 $\phi$-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. 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.