The high-temperature limit of the superconformal index, especially on higher sheets, often captures useful universal information about a theory. In 4d <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>2</mn> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N}=2 $</EquationSource> </InlineEquation> superconformal field theories with fractional r-charges, there exists a special notion of high-temperature limit on higher sheets that captures data of three-dimensional topological quantum field theories arising from r-twisted circle reduction. These TQFTs are closely tied with the VOA of the 4d SCFT. We study such high-temperature limits. More specifically, we apply Di Pietro-Komargodski type supersymmetric effective field theory techniques to r-twisted circle reductions of (A1, A2n) Argyres-Douglas theories, leveraging their Maruyoshi-Song Lagrangian with manifest <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N}=1 $</EquationSource> </InlineEquation> supersymmetry. The result on the second sheet is the Gang-Kim-Stubbs family of 3d <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>2</mn> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N}=2 $</EquationSource> </InlineEquation> SUSY enhancing rank-0 theories with monopole superpotentials, whose boundary supports the Virasoro minimal model VOAs M(2, 2n + 3). Upon topological twist, they give non-unitary TQFTs controlled by the M(2, 2n + 3) modular tensor category (MTC). The high-temperature limit on other sheets yields their unitary or non-unitary Galois conjugates. This opens up the prospect of a broader four-supercharge perspective on the celebrated correspondence between 4d <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>2</mn> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N}=2 $</EquationSource> </InlineEquation> SCFTs and 2d VOAs via interpolating 3d EFTs. Several byproducts follow, including a systematic approach to 3d SUSY enhancement from 4d SUSY enhancement, and a 3d QFT handle on Galois orbits of various MTCs associated with 4d <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>2</mn> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N}=2 $</EquationSource> </InlineEquation> SCFTs.

Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs

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2026年2月3日

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Arash Arabi Ardehali,
Mykola Dedushenko,
Dongmin Gang,
Mikhail Litvinov

摘要

The high-temperature limit of the superconformal index, especially on higher sheets, often captures useful universal information about a theory. In 4d $N = 2$ $ \mathcal{N}=2 $ superconformal field theories with fractional r-charges, there exists a special notion of high-temperature limit on higher sheets that captures data of three-dimensional topological quantum field theories arising from r-twisted circle reduction. These TQFTs are closely tied with the VOA of the 4d SCFT. We study such high-temperature limits. More specifically, we apply Di Pietro-Komargodski type supersymmetric effective field theory techniques to r-twisted circle reductions of (A₁, A_2n) Argyres-Douglas theories, leveraging their Maruyoshi-Song Lagrangian with manifest $N = 1$ $ \mathcal{N}=1 $ supersymmetry. The result on the second sheet is the Gang-Kim-Stubbs family of 3d $N = 2$ $ \mathcal{N}=2 $ SUSY enhancing rank-0 theories with monopole superpotentials, whose boundary supports the Virasoro minimal model VOAs M(2, 2n + 3). Upon topological twist, they give non-unitary TQFTs controlled by the M(2, 2n + 3) modular tensor category (MTC). The high-temperature limit on other sheets yields their unitary or non-unitary Galois conjugates. This opens up the prospect of a broader four-supercharge perspective on the celebrated correspondence between 4d $N = 2$ $ \mathcal{N}=2 $ SCFTs and 2d VOAs via interpolating 3d EFTs. Several byproducts follow, including a systematic approach to 3d SUSY enhancement from 4d SUSY enhancement, and a 3d QFT handle on Galois orbits of various MTCs associated with 4d $N = 2$ $ \mathcal{N}=2 $ SCFTs.