Supersymmetric quantum field theory with exotic symmetry in 3+1 dimensions and fermionic fracton phases

Abstract

We propose a supersymmetric quantum field theory with exotic symmetry related to fracton phases. We use superfield formalism and write down the action of a supersymmetric version of the theory in dimensions. It contains a large number of ground states due to the fermionic higher pole subsystem symmetry. Its residual entropy is proportional to the area instead of the volume. This theory has a self-duality similar to that of the theory. We also write down the action of a supersymmetric version of a tensor gauge theory, and discuss Bogomol'nyi-Prasad-Sommerfield (BPS) fractons.