We introduce a family of 3d <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\mathcal {N}=4$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> superconformal field theories that have zero-dimensional Coulomb and Higgs branches and propose that the rational vertex operator algebras <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$W^{\text{ min }}_{k - \scriptstyle {\frac{1}{2}}}(\mathfrak {sp}_{2N})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>W</mi> <mstyle displaystyle="false" scriptlevel="1"> <mrow> <mi>k</mi> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> <mrow> <mspace width="0.333333em" /> <mtext>min</mtext> <mspace width="0.333333em" /> </mrow> </msubsup> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="fraktur">sp</mi> <mrow> <mn>2</mn> <mi>N</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$L_{k}(\mathfrak {osp}_{1|2N})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mi>k</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="fraktur">osp</mi> <mrow> <mn>1</mn> <mo stretchy="false">|</mo> <mn>2</mn> <mi>N</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> model the modular tensor categories of line operators in their topological A and B twists, respectively. Our analysis indicates that the action of 3d mirror symmetry on this family of theories is related to a novel level-rank duality and leads to several conjectural q-series identities of independent interest.

Mirror symmetry and level-rank duality for 3d $\mathcal {N} = 4$ rank 0 SCFTs

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发表日期：

2025年10月31日

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Thomas Creutzig,
Niklas Garner,
Heeyeon Kim

摘要

We introduce a family of 3d $\mathcal {N}=4$ $N = 4$ superconformal field theories that have zero-dimensional Coulomb and Higgs branches and propose that the rational vertex operator algebras $W^{\text{ min }}_{k - \scriptstyle {\frac{1}{2}}}(\mathfrak {sp}_{2N})$ $W_{k - \frac{1}{2}}^{min} ({sp}_{2 N})$ and $L_{k}(\mathfrak {osp}_{1|2N})$ $L_{k} ({osp}_{1 | 2 N})$ model the modular tensor categories of line operators in their topological A and B twists, respectively. Our analysis indicates that the action of 3d mirror symmetry on this family of theories is related to a novel level-rank duality and leads to several conjectural q-series identities of independent interest.

Mirror symmetry and level-rank duality for 3d \(\mathcal {N} = 4\) rank 0 SCFTs

摘要