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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.11186 |
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| _version_ | 1866918264938954752 |
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| author | Kim, Heeyeon Kim, Hongseok Song, Jaewon |
| author_facet | Kim, Heeyeon Kim, Hongseok Song, Jaewon |
| contents | We propose a new fermionic sum formula for the Macdonald index of a class of Argyres-Douglas theories. The formula arises naturally from a three-dimensional topological field theory obtained via a twisted dimensional reduction of the 4d theory. Such a reduction often gives rise to a 3d ${\mathcal N}=2$ abelian Chern-Simons matter theory, which is expected to flow to an ${\mathcal N}=4$ superconformal fixed point. After performing a topological twist, we obtain a 3d TFT admitting boundary conditions that support the vertex operator algebra associated with the original 4d theory. In this framework, the Macdonald index appears as a half-index of the 3d gauge theory, with the Macdonald grading determined by a distinguished $U(1)_A$ symmetry in the infrared ${\mathcal N}=4$ superconformal algebra. We present a general procedure to identify this $U(1)_A$ symmetry and, whenever possible, show that it reproduces the refined character of the associated vertex operator algebra, thereby recovering the Macdonald index. Our construction also gives a hint towards the IR formula for the Macdonald index in terms of 4d BPS particles on the Coulomb branch. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11186 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Macdonald index from 3d TQFT Kim, Heeyeon Kim, Hongseok Song, Jaewon High Energy Physics - Theory We propose a new fermionic sum formula for the Macdonald index of a class of Argyres-Douglas theories. The formula arises naturally from a three-dimensional topological field theory obtained via a twisted dimensional reduction of the 4d theory. Such a reduction often gives rise to a 3d ${\mathcal N}=2$ abelian Chern-Simons matter theory, which is expected to flow to an ${\mathcal N}=4$ superconformal fixed point. After performing a topological twist, we obtain a 3d TFT admitting boundary conditions that support the vertex operator algebra associated with the original 4d theory. In this framework, the Macdonald index appears as a half-index of the 3d gauge theory, with the Macdonald grading determined by a distinguished $U(1)_A$ symmetry in the infrared ${\mathcal N}=4$ superconformal algebra. We present a general procedure to identify this $U(1)_A$ symmetry and, whenever possible, show that it reproduces the refined character of the associated vertex operator algebra, thereby recovering the Macdonald index. Our construction also gives a hint towards the IR formula for the Macdonald index in terms of 4d BPS particles on the Coulomb branch. |
| title | Macdonald index from 3d TQFT |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.11186 |