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This work demonstrates foliated-exotic duality in gapless ϕ-theories, revealing a novel anomaly inflow structure.
A bstract In this work, we construct a new foliated quantum field theory equivalent to the exotic ϕ -theory — a fractonic gapless scalar field theory described by tensor gauge fields and exhibiting U(1) × U(1) subsystem global symmetry. This subsystem symmetry has an ’t Hooft anomaly, which is captured by a subsystem symmetry-protected topological (SSPT) phase in one dimension higher via the anomaly inflow mechanism. By analyzing both the anomaly inflow structure and the foliated-exotic duality in the SSPT phases, we establish the foliated-exotic duality in the ϕ -theories. Furthermore, we also investigate the foliated-exotic duality in the φ̂ ϕ ̂ -theory, which is dual to the ϕ -theory, and construct the foliated φ̂ ϕ ̂ -theory. These are the first examples of the foliated-exotic duality in gapless theories.
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Ohmori et al. (2025) studied this question.
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