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

Masazumi HondaTaiichi Nakanishi
Dec 2022
摘要
We study various non-relativistic field theories with exotic symmetriescalled subsystem symmetries, which have recently attracted much attention inthe 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 andlattice regularization. Next we study a theory called chiral $\phi$-theorywhich is an analogue of a chiral boson with subsystem symmetries. Then wediscuss theories including fermions with subsystem symmetries. We firstconstruct a supersymmetric version of the $\phi$-theory and dropping itsbosonic part leads us to a purely fermionic theory with subsystem symmetriescalled $\psi$-theory. We argue that lattice regularization of the $\psi$-theorygenerically suffers from an analogue of doubling problem as previously pointedout in the $d=3$ case. We propose an analogue of Wilson fermion to avoid the``doubling" problem. We also supersymmetrize the chiral $\phi$-theory anddropping the bosonic part again gives us a purely fermionic theory. We finallydiscuss vacuum structures of the theories with fermions and find that they areinfinitely degenerate because of spontaneous breaking of subsystem symmetries.
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