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<p>In this work, we construct a new foliated quantum field theory equivalent to the exotic <i>ϕ</i>-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 <i>ϕ</i>-theories. Furthermore, we also investigate the foliated-exotic duality in the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27129_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi>ϕ</mi> <mo stretchy="true">̂</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( \hat{\phi} \)</EquationSource> </InlineEquation>-theory, which is dual to the <i>ϕ</i>-theory, and construct the foliated <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27129_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi>ϕ</mi> <mo stretchy="true">̂</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( \hat{\phi} \)</EquationSource> </InlineEquation>-theory. These are the first examples of the foliated-exotic duality in gapless theories.</p>

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Gapless foliated-exotic duality

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月5日

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  • Kantaro Ohmori,
  • Shutaro Shimamura

摘要

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 ϕ ̂ \( \hat{\phi} \) -theory, which is dual to the ϕ-theory, and construct the foliated ϕ ̂ \( \hat{\phi} \) -theory. These are the first examples of the foliated-exotic duality in gapless theories.