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We propose a supersymmetric quantum field theory with exotic symmetry relatedto fracton phases. We use superfield formalism and write down the action of asupersymmetric version of the $\varphi$ theory in 3+1 dimensions. It contains alarge number of ground states due to the fermionic higher pole subsystemsymmetry. Its residual entropy is proportional to the area instead of thevolume. This theory has a self-duality similar to that of the $\varphi$ theory.We also write down the action of a supersymmetric version of a tensor gaugetheory, and discuss BPS fractons.

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