<p>It has been recently shown that the celebrated SCFT<sub>4</sub>/VOA<sub>2</sub> correspondence can be bridged via three-dimensional field theories arising from a specific R-symmetry twisted circle reduction. We apply this twisted reduction to the (<i>A</i><sub>1</sub><i>, A</i><sub><i>n</i></sub>) and (<i>A</i><sub>1</sub><i>, D</i><sub><i>n</i></sub>) families of 4d <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27259_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>2</mn> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=2 \)</EquationSource> </InlineEquation> Argyres-Douglas SCFTs using their <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27259_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=1 \)</EquationSource> </InlineEquation> Agarwal-Maruyoshi-Song Lagrangians. From (<i>A</i><sub>1</sub><i>, A</i><sub>2<i>n</i></sub>) we derive the Gang-Kim-Stubbs family of 3d <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27259_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>2</mn> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=2 \)</EquationSource> </InlineEquation> gauge theories with SUSY enhancement to <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27259_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>4</mn> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=4 \)</EquationSource> </InlineEquation> in the infrared, generalizing a recent derivation made in the special cases <i>n</i> = 1<i>,</i> 2. Topological twists of these theories are known to yield <i>semisimple</i> TQFTs supporting <i>rational</i> VOAs on holomorphic boundaries. From (<i>A</i><sub>1</sub><i>, A</i><sub>2<i>n</i>−1</sub>), (<i>A</i><sub>1</sub><i>, D</i><sub>2<i>n</i>+1</sub>), and (<i>A</i><sub>1</sub><i>, D</i><sub>2<i>n</i></sub>), we obtain three new infinite families of 3d <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27259_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>2</mn> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=2 \)</EquationSource> </InlineEquation> abelian gauge theories, all with monopole superpotentials, flowing to <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27259_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>4</mn> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=4 \)</EquationSource> </InlineEquation> SCFTs without Coulomb branch, but with the same non-trivial Higgs branch as the four-dimensional parent. Their topological A-twist yields <i>non-semisimple</i> TQFTs related to <i>logarithmic</i> VOAs such as <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27259_Article_IEq7.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="66" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi mathvariant="italic">su</mi> <mo stretchy="true">̂</mo> </mover> <msub> <mfenced close=")" open="("> <mn>2</mn> </mfenced> <mrow> <mo>−</mo> <mn>4</mn> <mo>/</mo> <mn>3</mn> </mrow> </msub> </math></EquationSource> <EquationSource Format="TEX">\( \hat{su}{(2)}_{-4/3} \)</EquationSource> </InlineEquation>.</p>

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3d SUSY enhancement and non-semisimple TQFTs from four dimensions

  • Arash Arabi Ardehali,
  • Dongmin Gang,
  • Neville Joshua Rajappa,
  • Matteo Sacchi

摘要

It has been recently shown that the celebrated SCFT4/VOA2 correspondence can be bridged via three-dimensional field theories arising from a specific R-symmetry twisted circle reduction. We apply this twisted reduction to the (A1, An) and (A1, Dn) families of 4d N = 2 \( \mathcal{N}=2 \) Argyres-Douglas SCFTs using their N = 1 \( \mathcal{N}=1 \) Agarwal-Maruyoshi-Song Lagrangians. From (A1, A2n) we derive the Gang-Kim-Stubbs family of 3d N = 2 \( \mathcal{N}=2 \) gauge theories with SUSY enhancement to N = 4 \( \mathcal{N}=4 \) in the infrared, generalizing a recent derivation made in the special cases n = 1, 2. Topological twists of these theories are known to yield semisimple TQFTs supporting rational VOAs on holomorphic boundaries. From (A1, A2n−1), (A1, D2n+1), and (A1, D2n), we obtain three new infinite families of 3d N = 2 \( \mathcal{N}=2 \) abelian gauge theories, all with monopole superpotentials, flowing to N = 4 \( \mathcal{N}=4 \) SCFTs without Coulomb branch, but with the same non-trivial Higgs branch as the four-dimensional parent. Their topological A-twist yields non-semisimple TQFTs related to logarithmic VOAs such as su ̂ 2 4 / 3 \( \hat{su}{(2)}_{-4/3} \) .